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Volumn 1, Issue , 1996, Pages 3-26

Van der waerden conjecture and applications

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EID: 0009878908     PISSN: 15707954     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-7954(96)80005-2     Document Type: Chapter
Times cited : (3)

References (210)
  • 1
    • 0011606837 scopus 로고
    • To the theory of mixed volumes of convex bodies, I-IV
    • 1938
    • 1938. Alexandrov A.D. To the theory of mixed volumes of convex bodies, I-IV. Mat. Sb. 2 (1937) 947-972
    • (1937) Mat. Sb. , vol.2 , pp. 947-972
    • Alexandrov, A.D.1
  • 2
    • 0011332819 scopus 로고
    • To the theory of mixed volumes of convex bodies, I-IV
    • 1938
    • 1938. Alexandrov A.D. To the theory of mixed volumes of convex bodies, I-IV. Mat. Sb. 2 (1937) 1205-1238
    • (1937) Mat. Sb. , vol.2 , pp. 1205-1238
    • Alexandrov, A.D.1
  • 3
    • 0000864732 scopus 로고
    • To the theory of mixed volumes of convex bodies, I-IV
    • 1938
    • 1938. Alexandrov A.D. To the theory of mixed volumes of convex bodies, I-IV. Mat. Sb. 3 (1937) 27-46
    • (1937) Mat. Sb. , vol.3 , pp. 27-46
    • Alexandrov, A.D.1
  • 4
    • 0000864732 scopus 로고
    • To the theory of mixed volumes of convex bodies, I-IV
    • 1938. (in Russian)
    • 1938. Alexandrov A.D. To the theory of mixed volumes of convex bodies, I-IV. (in Russian). Mat. Sb. 3 (1937) 227-251
    • (1937) Mat. Sb. , vol.3 , pp. 227-251
    • Alexandrov, A.D.1
  • 5
    • 0014522689 scopus 로고
    • Series and parallel addition matrices
    • Anderson W.N., and Duffin R.J. Series and parallel addition matrices. J. Math. Anal. Appl. 26 (1969) 576-594
    • (1969) J. Math. Anal. Appl. , vol.26 , pp. 576-594
    • Anderson, W.N.1    Duffin, R.J.2
  • 6
    • 70350107941 scopus 로고
    • An inequality between symmetric function means of positive operators
    • Ando T. An inequality between symmetric function means of positive operators. Acta Sci. Math. 45 (1983) 19-22
    • (1983) Acta Sci. Math. , vol.45 , pp. 19-22
    • Ando, T.1
  • 7
    • 45149144980 scopus 로고
    • Majorization, doubly stochastic matrices, and comparison of eigenvalues
    • Ando T. Majorization, doubly stochastic matrices, and comparison of eigenvalues. Linear Algebra Appl. 118 (1989) 163-248
    • (1989) Linear Algebra Appl. , vol.118 , pp. 163-248
    • Ando, T.1
  • 8
    • 70350111530 scopus 로고
    • Some matrix inequalities in multiport network connections
    • Ando T., and Kubo F. Some matrix inequalities in multiport network connections. Oper. Theory Adv. Appl. 40 (1989) 111-131
    • (1989) Oper. Theory Adv. Appl. , vol.40 , pp. 111-131
    • Ando, T.1    Kubo, F.2
  • 9
    • 70350111532 scopus 로고
    • Inequalities among operator symmetric function means
    • Ando T., and Kubo F. Inequalities among operator symmetric function means. Proc. of Int. Symp. MTNS-89 vol. Ill (1990) 535-542
    • (1990) Proc. of Int. Symp. MTNS-89 , vol.Ill , pp. 535-542
    • Ando, T.1    Kubo, F.2
  • 10
    • 0041050442 scopus 로고
    • About one method of obtaining the lower estimates complexity of individual monotone functions
    • (in Russian)
    • (in Russian). Andreev A.E. About one method of obtaining the lower estimates complexity of individual monotone functions. Dokl. Akad. Nauk SSSR 282 (1985) 1033-1037
    • (1985) Dokl. Akad. Nauk SSSR , vol.282 , pp. 1033-1037
    • Andreev, A.E.1
  • 11
    • 70350101644 scopus 로고
    • On matrixfunctioner som med et numerisk little dificit viser v.d. Waerdens permanent hypothese
    • On matrix functions giving a good approximation to the Van der Waerden permanent conjecture, Preprint 30, Math. Inst., Kobenhavn. Turky
    • On matrix functions giving a good approximation to the Van der Waerden permanent conjecture, Preprint 30, Math. Inst., Kobenhavn. Bang T. On matrixfunctioner som med et numerisk little dificit viser v.d. Waerdens permanent hypothese. Proc. Scand. Congr. Turky (1976-1979)
    • (1979) Proc. Scand. Congr.
    • Bang, T.1
  • 12
    • 48749148777 scopus 로고
    • Doubly stochastic matrices with equal subpermanents
    • Bapat R.B. Doubly stochastic matrices with equal subpermanents. Linear Algebra Appl. 51 (1983) 1-8
    • (1983) Linear Algebra Appl. , vol.51 , pp. 1-8
    • Bapat, R.B.1
  • 13
    • 48549109691 scopus 로고
    • A stronger form of the Egorychev-Falikman theorem on permanents
    • Bapat R.B. A stronger form of the Egorychev-Falikman theorem on permanents. Linear Algebra Appl. 63 (1984) 95-100
    • (1984) Linear Algebra Appl. , vol.63 , pp. 95-100
    • Bapat, R.B.1
  • 14
    • 46149127706 scopus 로고
    • Inequalities for mixed Schur functions
    • Bapat R.B. Inequalities for mixed Schur functions. Linear Algebra Appl. 83 (1986) 143-149
    • (1986) Linear Algebra Appl. , vol.83 , pp. 143-149
    • Bapat, R.B.1
  • 15
    • 70350109717 scopus 로고
    • The multinomial distribution and permanents
    • Bapat R.B. The multinomial distribution and permanents. Linear Algebra Appl. 104 (1988) 201-205
    • (1988) Linear Algebra Appl. , vol.104 , pp. 201-205
    • Bapat, R.B.1
  • 16
    • 38249024073 scopus 로고
    • Mixed discriminants of positive semidefinite matrices
    • Bapat R.B. Mixed discriminants of positive semidefinite matrices. Linear Algebra Appl. 126 (1989) 107-124
    • (1989) Linear Algebra Appl. , vol.126 , pp. 107-124
    • Bapat, R.B.1
  • 18
    • 0009688514 scopus 로고
    • On majorization and Schur products
    • Bapat R.B., and Sunder V.S. On majorization and Schur products. Linear Algebra Appl. 72 (1985) 107-117
    • (1985) Linear Algebra Appl. , vol.72 , pp. 107-117
    • Bapat, R.B.1    Sunder, V.S.2
  • 19
    • 3242725567 scopus 로고
    • An extremal property of the permanent and the determinant
    • Bapat R.B., and Sunder V.S. An extremal property of the permanent and the determinant. Linear Algebra Appl. 76 (1986) 153-163
    • (1986) Linear Algebra Appl. , vol.76 , pp. 153-163
    • Bapat, R.B.1    Sunder, V.S.2
  • 20
    • 0010997233 scopus 로고
    • Theory of Möbius functions
    • (249). (in Russian)
    • (249). Barnabei M., Brini A., and Rota J.-C. Theory of Möbius functions. (in Russian). Uspekhi Mat. Nauk 41 3 (1986) 113-157
    • (1986) Uspekhi Mat. Nauk , vol.41 , Issue.3 , pp. 113-157
    • Barnabei, M.1    Brini, A.2    Rota, J.-C.3
  • 21
    • 34250406508 scopus 로고
    • The number of roots of a system of equations
    • Bernstein D.N. The number of roots of a system of equations. Functional Anal. Appl. 9 (1976) 183-185
    • (1976) Functional Anal. Appl. , vol.9 , pp. 183-185
    • Bernstein, D.N.1
  • 22
    • 0001495610 scopus 로고
    • A proof of McMullen's conditions for f-vectors of simplicial convex polytopes
    • Billera L.J., and Lee C.W. A proof of McMullen's conditions for f-vectors of simplicial convex polytopes. J. Combin. Theory Ser. A 31 (1981) 237-255
    • (1981) J. Combin. Theory Ser. A , vol.31 , pp. 237-255
    • Billera, L.J.1    Lee, C.W.2
  • 23
    • 40949124739 scopus 로고
    • Mémoire sur un système de formules analytiques, et leur application à des considérations géometriques
    • Binet J.P.M. Mémoire sur un système de formules analytiques, et leur application à des considérations géometriques. J. Éc. Polyt., 9. Cah. 16 (1812) 280-302
    • (1812) J. Éc. Polyt., 9. Cah. , vol.16 , pp. 280-302
    • Binet, J.P.M.1
  • 24
    • 0001336132 scopus 로고
    • Tres observaciones sobre el algebra lineal
    • Birkhoff G. Tres observaciones sobre el algebra lineal. Univ. Nac. Tucumán Rev., Ser A. 5 (1946) 147-151
    • (1946) Univ. Nac. Tucumán Rev., Ser A. , vol.5 , pp. 147-151
    • Birkhoff, G.1
  • 25
    • 70350120903 scopus 로고
    • Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function
    • Borchardt C.W. Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function. Monatsb. Akad. Wiss. Berlin (1855) 165-171
    • (1855) Monatsb. Akad. Wiss. Berlin , pp. 165-171
    • Borchardt, C.W.1
  • 26
    • 84929116955 scopus 로고
    • Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function
    • Borchardt C.W. Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function. Crelle's J. 53 (1855) 193-198
    • (1855) Crelle's J. , vol.53 , pp. 193-198
    • Borchardt, C.W.1
  • 27
    • 70350094889 scopus 로고
    • Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function
    • Borchardt C.W. Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function. Gesammelte Werke (1855) 97-105
    • (1855) Gesammelte Werke , pp. 97-105
    • Borchardt, C.W.1
  • 29
    • 0040330201 scopus 로고
    • Certain properties of non-negative matrices and their permanents
    • (in Russian)
    • (in Russian). Brégman L.M. Certain properties of non-negative matrices and their permanents. Dokl. Akad. Nauk SSSR 211 (1973) 27-30
    • (1973) Dokl. Akad. Nauk SSSR , vol.211 , pp. 27-30
    • Brégman, L.M.1
  • 30
    • 0002548740 scopus 로고
    • An interesting face of the polytope of doubly stochastic matrices
    • Brualdi R.A. An interesting face of the polytope of doubly stochastic matrices. Linear and Multilinear Algebra 17 (1985) 5-18
    • (1985) Linear and Multilinear Algebra , vol.17 , pp. 5-18
    • Brualdi, R.A.1
  • 31
    • 49449125391 scopus 로고
    • The convex polyhedron of doubly stochastic matrices, I. Applications of the permanent function
    • Brualdi R.A., and Gibson P.M. The convex polyhedron of doubly stochastic matrices, I. Applications of the permanent function. J. Combin. Theory Ser. A 22 (1977) 194-230
    • (1977) J. Combin. Theory Ser. A , vol.22 , pp. 194-230
    • Brualdi, R.A.1    Gibson, P.M.2
  • 32
    • 1842653674 scopus 로고
    • The many facets of combinatorial matrix theory
    • Brualdi R.A. The many facets of combinatorial matrix theory. Proc. Symp. Appl. Math. 40 (1990) 1-35
    • (1990) Proc. Symp. Appl. Math. , vol.40 , pp. 1-35
    • Brualdi, R.A.1
  • 33
  • 35
    • 51249194469 scopus 로고
    • On quantum field theory. I. Explicit solution of Dysons equation in electrodynamics without use of F ay man graphs
    • Caianiello E.R. On quantum field theory. I. Explicit solution of Dysons equation in electrodynamics without use of F ay man graphs. Nuovo Cimento 10 9 (1953) 1634-1652
    • (1953) Nuovo Cimento , vol.10 , Issue.9 , pp. 1634-1652
    • Caianiello, E.R.1
  • 36
    • 5344276734 scopus 로고
    • Properietá pfaffiani e hafniani
    • Caianiello E.R. Properietá pfaffiani e hafniani. Ricerca, Napoli 7 (1956) 25-31
    • (1956) Ricerca, Napoli , vol.7 , pp. 25-31
    • Caianiello, E.R.1
  • 37
    • 0039014428 scopus 로고
    • Mémoire sur les fonctions qui ne peuvent obtenir que deux valeurs égales et de signes contraires par suite des transpositions operées entre les variables qu'elles renferment
    • Oeuvres (2)i
    • Oeuvres (2)i. Cauchy A.L. Mémoire sur les fonctions qui ne peuvent obtenir que deux valeurs égales et de signes contraires par suite des transpositions operées entre les variables qu'elles renferment. J. Éc. Polyt., 10. Cah. 17 (1812) 29-112
    • (1812) J. Éc. Polyt., 10. Cah. , vol.17 , pp. 29-112
    • Cauchy, A.L.1
  • 38
    • 0040707600 scopus 로고
    • Hermitian matrix inequalities and a conjecture
    • Chan N.N., and Kwong M.K. Hermitian matrix inequalities and a conjecture. Amer. Math. Monthly 92 (1985) 533-541
    • (1985) Amer. Math. Monthly , vol.92 , pp. 533-541
    • Chan, N.N.1    Kwong, M.K.2
  • 39
    • 70350115417 scopus 로고
    • Notes on permanents of doubly stochastic matrices
    • Chang D.K. Notes on permanents of doubly stochastic matrices. Linear and Multilinear Algebra 14 (1983) 349-356
    • (1983) Linear and Multilinear Algebra , vol.14 , pp. 349-356
    • Chang, D.K.1
  • 40
    • 70350112757 scopus 로고
    • Minimum permanents of doubly stochastic matrices with one fixed entry
    • Chang D.K. Minimum permanents of doubly stochastic matrices with one fixed entry. Linear and Multilinear Algebra 15 (1984) 313-317
    • (1984) Linear and Multilinear Algebra , vol.15 , pp. 313-317
    • Chang, D.K.1
  • 41
    • 70350106039 scopus 로고
    • A note on a conjecture of T.H. Foregger
    • Chang D.K. A note on a conjecture of T.H. Foregger. Linear and Multilinear Algebra 15 (1984) 341-344
    • (1984) Linear and Multilinear Algebra , vol.15 , pp. 341-344
    • Chang, D.K.1
  • 42
    • 46149133142 scopus 로고
    • Permanents of doubly stochastic matrices
    • Chang D.K. Permanents of doubly stochastic matrices. Discrete Math. 62 (1986) 211-213
    • (1986) Discrete Math. , vol.62 , pp. 211-213
    • Chang, D.K.1
  • 43
    • 26444518195 scopus 로고
    • Is there a permanental analogue to Oppenheims inequality?
    • Chollet J. Is there a permanental analogue to Oppenheims inequality?. Amer. Math. Monthly 89 (1982) 57-58
    • (1982) Amer. Math. Monthly , vol.89 , pp. 57-58
    • Chollet, J.1
  • 45
    • 34250471395 scopus 로고
    • On pseudo-convex functions of non-negative variables
    • Cottle R.W., and Ferland J.A. On pseudo-convex functions of non-negative variables. Math. Programming 1 (1971) 95-101
    • (1971) Math. Programming , vol.1 , pp. 95-101
    • Cottle, R.W.1    Ferland, J.A.2
  • 46
    • 0039711846 scopus 로고
    • Matrix-theoretic criteria for the quasi-convexity and pseudo-convexity of quadratic functions
    • Cottle R.W., and Ferland J.A. Matrix-theoretic criteria for the quasi-convexity and pseudo-convexity of quadratic functions. Linear Algebra Appl. 5 (1972) 123-136
    • (1972) Linear Algebra Appl. , vol.5 , pp. 123-136
    • Cottle, R.W.1    Ferland, J.A.2
  • 48
    • 0041373461 scopus 로고
    • On a conjecture by van der Waerden
    • Docovic D.Z. On a conjecture by van der Waerden. Mat. Vesnik 4 (1967) 272-276
    • (1967) Mat. Vesnik , vol.4 , pp. 272-276
    • Docovic, D.Z.1
  • 50
    • 70350107939 scopus 로고
    • A note on the van der Waerden permanent conjecture
    • Dubois J. A note on the van der Waerden permanent conjecture. Can ad. J. Math. 6 (1974) 352-354
    • (1974) Can ad. J. Math. , vol.6 , pp. 352-354
    • Dubois, J.1
  • 51
    • 0005783699 scopus 로고
    • Remarks on the van der Waerden conjecture, II
    • Eberlein P.J. Remarks on the van der Waerden conjecture, II. Linear Algebra Appl. 2 (1969) 311-320
    • (1969) Linear Algebra Appl. , vol.2 , pp. 311-320
    • Eberlein, P.J.1
  • 52
    • 58149417501 scopus 로고
    • Some remarks on the van der Waerden conjecture
    • Eberlein P.J., and Mudholkar G.S. Some remarks on the van der Waerden conjecture. J. Combin. Theory 5 (1968) 386-396
    • (1968) J. Combin. Theory , vol.5 , pp. 386-396
    • Eberlein, P.J.1    Mudholkar, G.S.2
  • 54
    • 70350112762 scopus 로고
    • Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function
    • 1989, Amer. Math. Soc., Providence, RI
    • 1989. Borchardt C.W. Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function. Transi. Math. Monographs. 2nd ed. vol. 59 (1984), Amer. Math. Soc., Providence, RI
    • (1984) Transi. Math. Monographs. 2nd ed. , vol.59
    • Borchardt, C.W.1
  • 55
    • 66049111355 scopus 로고
    • Polynomial identity for the permanent
    • (in Russian)
    • (in Russian). Egorychev G.P. Polynomial identity for the permanent. Math. Zametki. 26 (1979) 961-964
    • (1979) Math. Zametki. , vol.26 , pp. 961-964
    • Egorychev, G.P.1
  • 56
    • 70350119058 scopus 로고
    • Family of identities for the permanent
    • (in Russian)
    • (in Russian). Egorychev G.P. Family of identities for the permanent. Dokl. Akad. Nauk Armenian SSR 69 (1979) 3-7
    • (1979) Dokl. Akad. Nauk Armenian SSR , vol.69 , pp. 3-7
    • Egorychev, G.P.1
  • 57
    • 70350122286 scopus 로고
    • The solution of problem Van der Waerden for permanents, Preprint, Inst. Fiziki Sibirsk. Otd. Akad. Nauk SSSR N 13M, Krasnoyarsk (in Russian). English transi
    • Egorychev G.P. The solution of problem Van der Waerden for permanents, Preprint, Inst. Fiziki Sibirsk. Otd. Akad. Nauk SSSR N 13M, Krasnoyarsk (in Russian). English transi. Adv. Math. 42 (1980) 299-305
    • (1980) Adv. Math. , vol.42 , pp. 299-305
    • Egorychev, G.P.1
  • 58
    • 66049115628 scopus 로고
    • New formulas for the permanent
    • (in Russian)
    • (in Russian). Egorychev G.P. New formulas for the permanent. Dokl. Akad. Nauk SSSR 254 (1980) 784-787
    • (1980) Dokl. Akad. Nauk SSSR , vol.254 , pp. 784-787
    • Egorychev, G.P.1
  • 59
    • 11544283160 scopus 로고
    • Proof of van der Waerden conjecture for permanents
    • Egorychev G.P. Proof of van der Waerden conjecture for permanents. Siberian Math. J. 22 (1981) 65-71
    • (1981) Siberian Math. J. , vol.22 , pp. 65-71
    • Egorychev, G.P.1
  • 60
    • 70350124232 scopus 로고
    • Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function
    • (in Russian)
    • (in Russian). Borchardt C.W. Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function. Dokl. Akad. Nauk SSSR 258 (1855) 1041-1044
    • (1855) Dokl. Akad. Nauk SSSR , vol.258 , pp. 1041-1044
    • Borchardt, C.W.1
  • 61
    • 70350104173 scopus 로고
    • History and proof of van der Waerden conjecture about permanents
    • (in Russian), Vyschtscha Shkola, Kiev
    • (in Russian). Egorychev G.P. History and proof of van der Waerden conjecture about permanents. Math. Today (1982), Vyschtscha Shkola, Kiev 44-75
    • (1982) Math. Today , pp. 44-75
    • Egorychev, G.P.1
  • 62
    • 70350112759 scopus 로고
    • Mixed discriminants and parallel addition
    • (in Russian)
    • (in Russian). Egorychev G.P. Mixed discriminants and parallel addition. Dokl. Akad. Nauk SSSR 312 (1990) 528-531
    • (1990) Dokl. Akad. Nauk SSSR , vol.312 , pp. 528-531
    • Egorychev, G.P.1
  • 63
    • 33745514520 scopus 로고
    • Mixed discriminants and parallel addition
    • English transi.
    • English transi. Egorychev G.P. Mixed discriminants and parallel addition. Soviet Math. Dokl. 41 (1990) 451-455
    • (1990) Soviet Math. Dokl. , vol.41 , pp. 451-455
    • Egorychev, G.P.1
  • 64
    • 70350115416 scopus 로고
    • Mixed discriminants in graph theory and electrotechnik
    • (in Russian), Mezhvuz. Sb., Krasn. Polytech. Inst., Krasnoyarsk
    • (in Russian). Egorychev G.P., and Moiseenko D.A. Mixed discriminants in graph theory and electrotechnik. Permanents: Theory and Applications (1990), Mezhvuz. Sb., Krasn. Polytech. Inst., Krasnoyarsk 138-157
    • (1990) Permanents: Theory and Applications , pp. 138-157
    • Egorychev, G.P.1    Moiseenko, D.A.2
  • 65
    • 70350112760 scopus 로고
    • 4-mixed discriminants and extremal problems for the permanent
    • 45 p. (in Russian)., Russian Akad. Nauk, Sverdlovsk
    • 45 p. (in Russian). Egorychev G.P. 4-mixed discriminants and extremal problems for the permanent. Conf. Math. Progr. and Appl., Ural Otd. (1993), Russian Akad. Nauk, Sverdlovsk
    • (1993) Conf. Math. Progr. and Appl., Ural Otd.
    • Egorychev, G.P.1
  • 67
    • 70350120898 scopus 로고
    • 1-14, (in Russian), Algebraic Systems, Sb. Computer Center of Sibirsk. Otd. Russian Akad. Nauk, Krasnoyarsk
    • 1-14, (in Russian). Egorychev G.P. Mixed discriminants on φ-addition (1994), Algebraic Systems, Sb. Computer Center of Sibirsk. Otd. Russian Akad. Nauk, Krasnoyarsk
    • (1994) Mixed discriminants on φ-addition
    • Egorychev, G.P.1
  • 68
    • 70350107933 scopus 로고    scopus 로고
    • Egorychev^G.P. and Ja.N.^Nuzhin, Permanents over distinct algebraic systems, In press.
    • Egorychev^G.P. and Ja.N.^Nuzhin, Permanents over distinct algebraic systems, In press.
  • 69
    • 70350120902 scopus 로고
    • G.P E., (Ed), Mezhvuz. Sb., Krasn. Polytech. Inst., Krasnoyarsk
    • In: G.P E., (Ed). Permanents: Theory and Applications (1990), Mezhvuz. Sb., Krasn. Polytech. Inst., Krasnoyarsk
    • (1990) Permanents: Theory and Applications
  • 70
    • 0039738285 scopus 로고
    • The asymptotic number of Latin rectangles
    • Erdôs P., and Kaplansky I. The asymptotic number of Latin rectangles. Amer. J. Math. 68 (1946) 230-236
    • (1946) Amer. J. Math. , vol.68 , pp. 230-236
    • Erdôs, P.1    Kaplansky, I.2
  • 71
    • 70350124229 scopus 로고
    • A new operation for analyzing series parallel networks
    • Erickson K.E. A new operation for analyzing series parallel networks. IEEE Trans. Theory CT-6 (1959) 124-126
    • (1959) IEEE Trans. Theory , vol.CT-6 , pp. 124-126
    • Erickson, K.E.1
  • 72
    • 70350117295 scopus 로고
    • Convex bodies and algebraic geometry
    • Ewald G. Convex bodies and algebraic geometry. Ann. New York Acad. Sci. 440 (1985) 196-204
    • (1985) Ann. New York Acad. Sci. , vol.440 , pp. 196-204
    • Ewald, G.1
  • 73
    • 0001255036 scopus 로고
    • Proof of van der Waerden conjecture about permanent of doubly stochastic matrix
    • (in Russian)
    • (in Russian). Falikman D.I. Proof of van der Waerden conjecture about permanent of doubly stochastic matrix. Mat. Zametki 29 (1981) 931-938
    • (1981) Mat. Zametki , vol.29 , pp. 931-938
    • Falikman, D.I.1
  • 74
    • 0011484987 scopus 로고
    • Inégalités quadratiques entre les volumes mixtes des corps convexes
    • Fenchel W. Inégalités quadratiques entre les volumes mixtes des corps convexes. C. R. Acad. Sci. Paris 203 (1936) 647-650
    • (1936) C. R. Acad. Sci. Paris , vol.203 , pp. 647-650
    • Fenchel, W.1
  • 75
    • 49149148328 scopus 로고
    • Positive subdefinite matrices
    • Ferland J.A. Positive subdefinite matrices. Linear Algebra Appl. 31 (1980) 233-244
    • (1980) Linear Algebra Appl. , vol.31 , pp. 233-244
    • Ferland, J.A.1
  • 77
    • 70350096704 scopus 로고
    • On facial minimizing matrices for the permanent functions
    • Foregger T.H. On facial minimizing matrices for the permanent functions. Notices Amer. Math. Soc. Ser. A 21 (1974) 434
    • (1974) Notices Amer. Math. Soc. Ser. A , vol.21 , pp. 434
    • Foregger, T.H.1
  • 78
    • 0002672220 scopus 로고
    • On the minimum value of the permanent of a nearly decomposable doubly stochastic matrix
    • Foregger T.H. On the minimum value of the permanent of a nearly decomposable doubly stochastic matrix. Linear Algebra Appl. 32 (1980) 75-85
    • (1980) Linear Algebra Appl. , vol.32 , pp. 75-85
    • Foregger, T.H.1
  • 79
    • 18844441069 scopus 로고
    • Minimum permanents of multiplexes
    • Foregger T.H. Minimum permanents of multiplexes. Linear Algebra Appl. 87 (1987) 197-211
    • (1987) Linear Algebra Appl. , vol.87 , pp. 197-211
    • Foregger, T.H.1
  • 80
    • 18844404273 scopus 로고
    • On matrices minimizing the permanent on faces of the poyhedrom of the doubly stochastic matrices
    • Foregger T.H., and Sinkhorn R. On matrices minimizing the permanent on faces of the poyhedrom of the doubly stochastic matrices. Linear and Multilinear Algebra 19 (1986) 395-397
    • (1986) Linear and Multilinear Algebra , vol.19 , pp. 395-397
    • Foregger, T.H.1    Sinkhorn, R.2
  • 81
    • 70350120901 scopus 로고
    • The polynomial identities and invariants of n x n matrices
    • Formanek E. The polynomial identities and invariants of n x n matrices. Notices Amer. Math. Soc. 38 (1991) 150
    • (1991) Notices Amer. Math. Soc. , vol.38 , pp. 150
    • Formanek, E.1
  • 82
    • 0016353146 scopus 로고
    • Matrices satisfying the van der Waerden conjecture
    • Friedland S. Matrices satisfying the van der Waerden conjecture. Linear Algebra Appl. 8 (1974) 521-528
    • (1974) Linear Algebra Appl. , vol.8 , pp. 521-528
    • Friedland, S.1
  • 83
    • 41749122404 scopus 로고
    • A study of the van der Waerden conjecture and its generalization
    • Friedland S. A study of the van der Waerden conjecture and its generalization. Linear and Multilinear Algebra 6 (1978) 123-143
    • (1978) Linear and Multilinear Algebra , vol.6 , pp. 123-143
    • Friedland, S.1
  • 84
    • 0012963385 scopus 로고
    • A lower bound for the permanent of a doubly stochastic matrix
    • Friedland S. A lower bound for the permanent of a doubly stochastic matrix. Ann. Math. 110 (1979) 167-176
    • (1979) Ann. Math. , vol.110 , pp. 167-176
    • Friedland, S.1
  • 86
    • 0041373452 scopus 로고
    • A proof of generalized van der Waerden conjecture on permanents
    • Friedland S. A proof of generalized van der Waerden conjecture on permanents. Linear and Multilinear Algebra 11 (1982) 107-120
    • (1982) Linear and Multilinear Algebra , vol.11 , pp. 107-120
    • Friedland, S.1
  • 88
    • 34250087314 scopus 로고
    • On a combinatorial problem related to permanents
    • Fröberg C.-E. On a combinatorial problem related to permanents. BIT 28 (1988) 406-411
    • (1988) BIT , vol.28 , pp. 406-411
    • Fröberg, C.-E.1
  • 92
    • 70350104171 scopus 로고
    • Inequalities for hyperbolic polynoms
    • (in Russian)
    • (in Russian). Gasparjan A.S. Inequalities for hyperbolic polynoms. Dokl. Akad. Nauk SSSR 276 (1984) 1294-1296
    • (1984) Dokl. Akad. Nauk SSSR , vol.276 , pp. 1294-1296
    • Gasparjan, A.S.1
  • 93
    • 84968476158 scopus 로고
    • Counting Latin rectangles
    • Gessel I. Counting Latin rectangles. Bull. Amer. Math. Soc. 16 (1987) 79-82
    • (1987) Bull. Amer. Math. Soc. , vol.16 , pp. 79-82
    • Gessel, I.1
  • 94
    • 0042822763 scopus 로고
    • Permanental polytopes of doubly stochastic matrices
    • Gibson P.M. Permanental polytopes of doubly stochastic matrices. Linear Algebra Appl. 12 (1980) 87-111
    • (1980) Linear Algebra Appl. , vol.12 , pp. 87-111
    • Gibson, P.M.1
  • 95
    • 58149416086 scopus 로고
    • Remarks on the van der Waerden permanent conjecture
    • Gleason A.M. Remarks on the van der Waerden permanent conjecture. J. Combin. Theory 8 (1970) 54-64
    • (1970) J. Combin. Theory , vol.8 , pp. 54-64
    • Gleason, A.M.1
  • 98
    • 0042136058 scopus 로고
    • Permanental inequalities for correlation matrices
    • Grone R., and Pierce S. Permanental inequalities for correlation matrices. SIAM J. Matrix Anal. Appl. 9 (1988) 194-201
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 194-201
    • Grone, R.1    Pierce, S.2
  • 99
    • 0242401293 scopus 로고
    • Gruber P.M., and Wills J.M. (Eds), Birkhäuser, Basel
    • In: Gruber P.M., and Wills J.M. (Eds). Convexity and Its Applications (1983), Birkhäuser, Basel
    • (1983) Convexity and Its Applications
  • 100
    • 70350117295 scopus 로고
    • Convex bodies and algebraic geometry. Discrete geometry and convexity
    • Günter E. Convex bodies and algebraic geometry. Discrete geometry and convexity. Ann. New York Acad. Sci. 440 (1985) 196-204
    • (1985) Ann. New York Acad. Sci. , vol.440 , pp. 196-204
    • Günter, E.1
  • 101
    • 70350094888 scopus 로고
    • On permanent inequalities
    • Combinatorics
    • Combinatorics. Gyires B. On permanent inequalities. Coll. Math. Soc. Jänos Bolyai vol. 18 (1976)
    • (1976) Coll. Math. Soc. Jänos Bolyai , vol.18
    • Gyires, B.1
  • 102
    • 84971138052 scopus 로고
    • An improved lower bound for the multidimensional dimer problem
    • Hammersley J.M. An improved lower bound for the multidimensional dimer problem. Proc. Cambridge Philos. Soc. 64 (1968) 455-463
    • (1968) Proc. Cambridge Philos. Soc. , vol.64 , pp. 455-463
    • Hammersley, J.M.1
  • 104
    • 0348104610 scopus 로고
    • Determinants, permanents and bipartite graphs
    • Harary F. Determinants, permanents and bipartite graphs. Math. Mag. 42 (1969) 146-148
    • (1969) Math. Mag. , vol.42 , pp. 146-148
    • Harary, F.1
  • 105
    • 84968492800 scopus 로고
    • A simplified form for nearly reducible and nearly decomposable matrices
    • Hartfiel D.J. A simplified form for nearly reducible and nearly decomposable matrices. Proc. Amer. Math. Soc. 24 (1970) 388-393
    • (1970) Proc. Amer. Math. Soc. , vol.24 , pp. 388-393
    • Hartfiel, D.J.1
  • 106
    • 84968481056 scopus 로고
    • A role for doubly stochastic matrices in graph theory
    • Hartfiel D.J., and Spellman J.W. A role for doubly stochastic matrices in graph theory. Proc. Amer. Math. Soc. 36 (1972) 389-394
    • (1972) Proc. Amer. Math. Soc. , vol.36 , pp. 389-394
    • Hartfiel, D.J.1    Spellman, J.W.2
  • 107
    • 0001662527 scopus 로고
    • Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes
    • Höchster M. Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes. Ann. Math. 96 (1972) 318-337
    • (1972) Ann. Math. , vol.96 , pp. 318-337
    • Höchster, M.1
  • 108
    • 0040569848 scopus 로고
    • Two aspects of doubly stochastic matrices: permutation matrices and the minimum of the permanent function (Thesis abstract)
    • Holens F. Two aspects of doubly stochastic matrices: permutation matrices and the minimum of the permanent function (Thesis abstract). Canad. Math. Bull. 7 (1964) 509-510
    • (1964) Canad. Math. Bull. , vol.7 , pp. 509-510
    • Holens, F.1
  • 109
    • 27544504822 scopus 로고
    • Analogs of Alexandrov-Fenchel inequalities for hyperbolic forms
    • (in Russian)
    • (in Russian). Hovansky A.G. Analogs of Alexandrov-Fenchel inequalities for hyperbolic forms. Dokl. Akad. Nauk SSSR 276 (1984) 1332-1334
    • (1984) Dokl. Akad. Nauk SSSR , vol.276 , pp. 1332-1334
    • Hovansky, A.G.1
  • 110
    • 0010784243 scopus 로고
    • Minimum permanent on faces of stair-case type of the polytope of doubly stochastic matrices
    • Hwang S.G. Minimum permanent on faces of stair-case type of the polytope of doubly stochastic matrices. Linear and Multilinear Algebra 18 (1985) 271-306
    • (1985) Linear and Multilinear Algebra , vol.18 , pp. 271-306
    • Hwang, S.G.1
  • 111
    • 34648849195 scopus 로고
    • A note on a conjecture on permanents
    • Hwang S.G. A note on a conjecture on permanents. Linear Algebra Appl. 76 (1986) 31-44
    • (1986) Linear Algebra Appl. , vol.76 , pp. 31-44
    • Hwang, S.G.1
  • 112
    • 0041874221 scopus 로고
    • The monotonicity and the Dokovic conjectures on permanents of doubly stochastic matrices
    • Hwang S.G. The monotonicity and the Dokovic conjectures on permanents of doubly stochastic matrices. Linear Algebra Appl. 79 (1986) 127-151
    • (1986) Linear Algebra Appl. , vol.79 , pp. 127-151
    • Hwang, S.G.1
  • 113
    • 18844423149 scopus 로고
    • On a conjecture of E. Dittert
    • Hwang S.G. On a conjecture of E. Dittert. Linear Algebra Appl. 95 (1987) 161-169
    • (1987) Linear Algebra Appl. , vol.95 , pp. 161-169
    • Hwang, S.G.1
  • 114
    • 84966224656 scopus 로고
    • On the monotonicity of the permanent
    • Hwang S.G. On the monotonicity of the permanent. Proc. Amer. Math. Soc. 106 (1989) 59-63
    • (1989) Proc. Amer. Math. Soc. , vol.106 , pp. 59-63
    • Hwang, S.G.1
  • 116
    • 70350101639 scopus 로고
    • Vegues terfogat es a van der Waerden's sejtes
    • 1981
    • 1981. Janos P. Vegues terfogat es a van der Waerden's sejtes. Mat. Lapok 29 (1977) 46-60
    • (1977) Mat. Lapok , vol.29 , pp. 46-60
    • Janos, P.1
  • 117
    • 5644245757 scopus 로고
    • Combinatorial matrix analysis and overview
    • Johnston C.R. Combinatorial matrix analysis and overview. Linear Algebra Appl. 107 (1988) 3-15
    • (1988) Linear Algebra Appl. , vol.107 , pp. 3-15
    • Johnston, C.R.1
  • 120
    • 9144267154 scopus 로고
    • Entropy inequalities for classes of probability distributions, II. The multivariate case
    • Karlin S., and Rinott Y. Entropy inequalities for classes of probability distributions, II. The multivariate case. Adv. Appl. Probab. 13 (1981) 325-351
    • (1981) Adv. Appl. Probab. , vol.13 , pp. 325-351
    • Karlin, S.1    Rinott, Y.2
  • 122
    • 0039718590 scopus 로고
    • Schälbare Cohen-Macaulay-Komplexe und ihre Parametriesierung
    • Kind B., and Kleinschmidt P. Schälbare Cohen-Macaulay-Komplexe und ihre Parametriesierung. Math. Z. 167 (1979) 173-179
    • (1979) Math. Z. , vol.167 , pp. 173-179
    • Kind, B.1    Kleinschmidt, P.2
  • 123
    • 0038983464 scopus 로고
    • Minimum permanents of doubly stochastic matrices with at least one zero entry
    • Knopp P., and Sinkhorn R. Minimum permanents of doubly stochastic matrices with at least one zero entry. Linear and Multilinear Algebra 11 (1982) 351-355
    • (1982) Linear and Multilinear Algebra , vol.11 , pp. 351-355
    • Knopp, P.1    Sinkhorn, R.2
  • 124
    • 65349158495 scopus 로고
    • A permanent inequality
    • Knuth D. A permanent inequality. Amer. Math. Monthly 88 (1981) 731-740
    • (1981) Amer. Math. Monthly , vol.88 , pp. 731-740
    • Knuth, D.1
  • 125
    • 14244256152 scopus 로고
    • Polyèdres de Newton et nombres de Milnor
    • Kouchnirenko A.G. Polyèdres de Newton et nombres de Milnor. Invent. Math. 32 (1976) 1-31
    • (1976) Invent. Math. , vol.32 , pp. 1-31
    • Kouchnirenko, A.G.1
  • 126
    • 34250966677 scopus 로고
    • Über Graphen und ihre Anwendung auf Determinantentheorie und Mengelehre
    • König D. Über Graphen und ihre Anwendung auf Determinantentheorie und Mengelehre. Math. Ann 77 (1916) 453-465
    • (1916) Math. Ann , vol.77 , pp. 453-465
    • König, D.1
  • 128
    • 0009299956 scopus 로고
    • Some results on matrix monotone functions
    • Kwong M.K. Some results on matrix monotone functions. Linear Algebra Appl. 118 (1989) 129-153
    • (1989) Linear Algebra Appl. , vol.118 , pp. 129-153
    • Kwong, M.K.1
  • 129
    • 65349097842 scopus 로고
    • The van der Waerden conjecture: two Soviet solutions
    • Lagans J.C. The van der Waerden conjecture: two Soviet solutions. Notices Amer. Math. Soc. 29 (1982) 130-133
    • (1982) Notices Amer. Math. Soc. , vol.29 , pp. 130-133
    • Lagans, J.C.1
  • 130
    • 0004257620 scopus 로고
    • VEB Deutscher Verlag der Wissenschaften, Berlin
    • Leichtweiss K. Konvexe Mengen (1980), VEB Deutscher Verlag der Wissenschaften, Berlin
    • (1980) Konvexe Mengen
    • Leichtweiss, K.1
  • 131
    • 0001403189 scopus 로고
    • Proofs of some conjectures on permanents
    • Lieb E.H. Proofs of some conjectures on permanents. J. Math. Mech. 16 (1966) 127-134
    • (1966) J. Math. Mech. , vol.16 , pp. 127-134
    • Lieb, E.H.1
  • 132
    • 0347310578 scopus 로고
    • Notices on Egoritsjev's proof of the van der Waerden conjecture
    • Lint v.J.H. Notices on Egoritsjev's proof of the van der Waerden conjecture. Linear Algebra Appl. 39 (1981) 1-8
    • (1981) Linear Algebra Appl. , vol.39 , pp. 1-8
    • Lint, v.J.H.1
  • 133
    • 33748476970 scopus 로고
    • The van der Waerden conjecture: two proofs in one year
    • Lint van J.H. The van der Waerden conjecture: two proofs in one year. Math. Intelligencer 4 (1982) 72-77
    • (1982) Math. Intelligencer , vol.4 , pp. 72-77
    • Lint van, J.H.1
  • 134
    • 33748464514 scopus 로고
    • The van der Waerden conjecture
    • Lint v.J.H. The van der Waerden conjecture. Ann. Discrete Math. 18 (1983) 575-580
    • (1983) Ann. Discrete Math. , vol.18 , pp. 575-580
    • Lint, v.J.H.1
  • 135
    • 0002909412 scopus 로고
    • Some notes on the van der Waerden conjecture
    • London D. Some notes on the van der Waerden conjecture. Linear Algebra Appl. 4 (1971) 155-160
    • (1971) Linear Algebra Appl. , vol.4 , pp. 155-160
    • London, D.1
  • 136
    • 0041373455 scopus 로고
    • On the Doković conjecture for matrices of rank two
    • London D. On the Doković conjecture for matrices of rank two. Linear and Multilinear Algebra 9 (1981) 317-327
    • (1981) Linear and Multilinear Algebra , vol.9 , pp. 317-327
    • London, D.1
  • 137
    • 43849096290 scopus 로고
    • On the van der Waerden conjecture and zeros of polynomials
    • London D. On the van der Waerden conjecture and zeros of polynomials. Linear Algebra Appl. 45 (1982) 35-41
    • (1982) Linear Algebra Appl. , vol.45 , pp. 35-41
    • London, D.1
  • 138
    • 0041373453 scopus 로고
    • On the permanent of doubly stochastic matrices with zero diagonal
    • London D., and Minc H. On the permanent of doubly stochastic matrices with zero diagonal. Linear and Multilinear Algebra 24 (1989) 289-300
    • (1989) Linear and Multilinear Algebra , vol.24 , pp. 289-300
    • London, D.1    Minc, H.2
  • 139
    • 51249175744 scopus 로고
    • Rotation means of projections
    • Lutwak E. Rotation means of projections. Israel J. Math. Sci. 58 (1987) 161-169
    • (1987) Israel J. Math. Sci. , vol.58 , pp. 161-169
    • Lutwak, E.1
  • 140
    • 0000830163 scopus 로고
    • Intersection bodies and dual mixed volumes
    • Lutwak E. Intersection bodies and dual mixed volumes. Adv. Math. 71 (1988) 232-261
    • (1988) Adv. Math. , vol.71 , pp. 232-261
    • Lutwak, E.1
  • 141
    • 70350124226 scopus 로고
    • Centroid bodies and dual mixed volumes
    • Lutwak E. Centroid bodies and dual mixed volumes. Proc. London Math. Soc. 60 (1990) 1-27
    • (1990) Proc. London Math. Soc. , vol.60 , pp. 1-27
    • Lutwak, E.1
  • 144
    • 84974127272 scopus 로고
    • On a conjecture of B.L. van der Waerden
    • Marcus M., and Minc H. On a conjecture of B.L. van der Waerden. Proc. Cambridge Philos. Soc. 63 (1967) 305-309
    • (1967) Proc. Cambridge Philos. Soc. , vol.63 , pp. 305-309
    • Marcus, M.1    Minc, H.2
  • 145
    • 65349104697 scopus 로고
    • On the minimum on the permanent of a doubly stochastic matrix
    • Marcus M., and Newman M. On the minimum on the permanent of a doubly stochastic matrix. Duke Math. J. 26 (1959) 61-72
    • (1959) Duke Math. J. , vol.26 , pp. 61-72
    • Marcus, M.1    Newman, M.2
  • 146
    • 0038086976 scopus 로고
    • Scaling of matrices to achieve specified row and column sums
    • Marshall A.W., and Olkin J. Scaling of matrices to achieve specified row and column sums. Num. Math. 12 (1968) 83-90
    • (1968) Num. Math. , vol.12 , pp. 83-90
    • Marshall, A.W.1    Olkin, J.2
  • 148
    • 0014596224 scopus 로고
    • Subdefinite matrices and quadratic forms
    • Martos B. Subdefinite matrices and quadratic forms. SIAM J. Appl. Math. 17 (1969) 1215-1223
    • (1969) SIAM J. Appl. Math. , vol.17 , pp. 1215-1223
    • Martos, B.1
  • 149
    • 62649104532 scopus 로고
    • Quadratic programming with a quasi-convex objective function
    • Martos B. Quadratic programming with a quasi-convex objective function. Oper. Res. 19 (1971) 87-97
    • (1971) Oper. Res. , vol.19 , pp. 87-97
    • Martos, B.1
  • 150
    • 38249027258 scopus 로고
    • Some possible new directions for combinatorial matrix analysis
    • Maybee J.S. Some possible new directions for combinatorial matrix analysis. Linear Algebra Appl. 107 (1988) 23-40
    • (1988) Linear Algebra Appl. , vol.107 , pp. 23-40
    • Maybee, J.S.1
  • 153
    • 62749107753 scopus 로고
    • On the partial ordering of parallel summable matrices
    • Meenakshi A.R. On the partial ordering of parallel summable matrices. Houston J. Math. 13 (1987) 255-262
    • (1987) Houston J. Math. , vol.13 , pp. 255-262
    • Meenakshi, A.R.1
  • 154
    • 0040928045 scopus 로고
    • The permanental dominance conjecture
    • Elsevier, New York
    • Merris R. The permanental dominance conjecture. Current Trends in Matrix Theory (1987), Elsevier, New York 213-223
    • (1987) Current Trends in Matrix Theory , pp. 213-223
    • Merris, R.1
  • 155
    • 34250122797 scopus 로고
    • Interpolation of scattered data: distance matrices and conditionally positive definite matrices
    • Micchelli C.A. Interpolation of scattered data: distance matrices and conditionally positive definite matrices. Constr. Approx. 2 (1986) 11-22
    • (1986) Constr. Approx. , vol.2 , pp. 11-22
    • Micchelli, C.A.1
  • 156
    • 70350096702 scopus 로고
    • Subpermanents of doubly stochastic matrices
    • Minc H. Subpermanents of doubly stochastic matrices. Linear and Multilinear Algebra 3 (1975) 91-94
    • (1975) Linear and Multilinear Algebra , vol.3 , pp. 91-94
    • Minc, H.1
  • 158
    • 0040322062 scopus 로고
    • An upper bound for the multidimensional dimer problem
    • Minc H. An upper bound for the multidimensional dimer problem. Math. Proc. Cambridge Phil. Soc. 83 (1978) 461-462
    • (1978) Math. Proc. Cambridge Phil. Soc. , vol.83 , pp. 461-462
    • Minc, H.1
  • 159
    • 70350091806 scopus 로고
    • An asymptotic solution of the multidimensional dimer problem
    • Minc H. An asymptotic solution of the multidimensional dimer problem. Linear and Multilinear Algebra 8 (1980) 235-239
    • (1980) Linear and Multilinear Algebra , vol.8 , pp. 235-239
    • Minc, H.1
  • 160
    • 70350117299 scopus 로고
    • A note on Egorycev's proof of the van der Waerden conjecture
    • Minc H. A note on Egorycev's proof of the van der Waerden conjecture. Linear and Multilinear Algebra 111 (1982) 367-371
    • (1982) Linear and Multilinear Algebra , vol.111 , pp. 367-371
    • Minc, H.1
  • 161
    • 0000773629 scopus 로고
    • Theory of permanents 1978-1981
    • Minc H. Theory of permanents 1978-1981. Linear and Multilinear Algebra 12 (1983) 227-263
    • (1983) Linear and Multilinear Algebra , vol.12 , pp. 227-263
    • Minc, H.1
  • 162
    • 0001848178 scopus 로고
    • Minimum permanents of doubly stochastic matrices with prescribed zero entries
    • Minc H. Minimum permanents of doubly stochastic matrices with prescribed zero entries. Linear and Multilinear Algebra 15 (1984) 225-243
    • (1984) Linear and Multilinear Algebra , vol.15 , pp. 225-243
    • Minc, H.1
  • 163
    • 84947882873 scopus 로고
    • Theory of permanents 1982-1985
    • Minc H. Theory of permanents 1982-1985. Linear and Multilinear Algebra 21 (1987) 109-148
    • (1987) Linear and Multilinear Algebra , vol.21 , pp. 109-148
    • Minc, H.1
  • 165
    • 0039480862 scopus 로고
    • Theorie der convexen Körper, unsbesondere Bergundung ihres Oberflachenbegriffs
    • Leipzig-Berlin
    • Leipzig-Berlin. Minkowsky H. Theorie der convexen Körper, unsbesondere Bergundung ihres Oberflachenbegriffs. Ges. Abh. B. 2 (1911) 131-229
    • (1911) Ges. Abh. B. , vol.2 , pp. 131-229
    • Minkowsky, H.1
  • 166
    • 0041182358 scopus 로고
    • Matrix partial orders through generalized inverses: unified theory
    • Mitra S.K. Matrix partial orders through generalized inverses: unified theory. Linear Algebra Appl. 148 (1991) 237-263
    • (1991) Linear Algebra Appl. , vol.148 , pp. 237-263
    • Mitra, S.K.1
  • 169
    • 70350106037 scopus 로고
    • About signature and kernel of bilinear form connected with permanent
    • (in Russian)
    • (in Russian). Panov A.A. About signature and kernel of bilinear form connected with permanent. Uspekhi Mat. Nauk 39 (1984) 202
    • (1984) Uspekhi Mat. Nauk , vol.39 , pp. 202
    • Panov, A.A.1
  • 170
    • 33846652710 scopus 로고
    • About mixed discriminants connected with positive semidefinite quadratic forms
    • (in Russian)
    • (in Russian). Panov A.A. About mixed discriminants connected with positive semidefinite quadratic forms. Dokl. Akad. Nauk SSSR 282 (1985) 273-276
    • (1985) Dokl. Akad. Nauk SSSR , vol.282 , pp. 273-276
    • Panov, A.A.1
  • 171
    • 0040928043 scopus 로고
    • Permanental dominance and the Soules conjecture for certain right ideals in the group algebra
    • Pate T.H. Permanental dominance and the Soules conjecture for certain right ideals in the group algebra. Linear and Multilinear Algebra 24 (1989) 135-149
    • (1989) Linear and Multilinear Algebra , vol.24 , pp. 135-149
    • Pate, T.H.1
  • 173
    • 70350098558 scopus 로고
    • Permanents of correlation matrices
    • Elsevier, Amsterdam
    • Pierce S. Permanents of correlation matrices. Current Trends in Matrix Theory (1987), Elsevier, Amsterdam
    • (1987) Current Trends in Matrix Theory
    • Pierce, S.1
  • 174
    • 35348893043 scopus 로고
    • Seven kinds of convexity
    • Ponstein J. Seven kinds of convexity. SIAM Rev. 9 (1967) 115-119
    • (1967) SIAM Rev. , vol.9 , pp. 115-119
    • Ponstein, J.1
  • 175
    • 70350117297 scopus 로고
    • On even doubly stochastic matrices with minimal even permanent
    • Rammer A. On even doubly stochastic matrices with minimal even permanent. Acta Commentat. Universitatis 878 (1990) 103-114
    • (1990) Acta Commentat. Universitatis , vol.878 , pp. 103-114
    • Rammer, A.1
  • 176
    • 0037909270 scopus 로고
    • Lower estimates of monotone complexity of logic permanent
    • (in Russian)
    • (in Russian). Razborov A.A. Lower estimates of monotone complexity of logic permanent. Mat. Zametki 37 (1985) 887-900
    • (1985) Mat. Zametki , vol.37 , pp. 887-900
    • Razborov, A.A.1
  • 180
    • 51649174670 scopus 로고
    • Study of the permanent conjecture and some of its generalizations
    • Rothaus O.S. Study of the permanent conjecture and some of its generalizations. Israel J. Math. 18 (1974) 75-96.
    • (1974) Israel J. Math. , vol.18
    • Rothaus, O.S.1
  • 183
    • 58149413061 scopus 로고
    • On the inequality 25-01 and the van der Waerden conjecture
    • Sasser D.W., and Slater M.L. On the inequality 25-01 and the van der Waerden conjecture. J. Combin. Theory 3 (1967) 25-33
    • (1967) J. Combin. Theory , vol.3 , pp. 25-33
    • Sasser, D.W.1    Slater, M.L.2
  • 185
    • 21744451525 scopus 로고
    • On A.D. Alexandrovs inequalities for mixed discriminants
    • Schneider R. On A.D. Alexandrovs inequalities for mixed discriminants. J. Math. Mech. 15 (1966) 285-290
    • (1966) J. Math. Mech. , vol.15 , pp. 285-290
    • Schneider, R.1
  • 186
    • 70350088745 scopus 로고
    • Permanents and the problem of planar graphs coloring
    • (in Russian), Mezhvuz. Sb., Krasn. Polytechn. Inst., Krasnoyarsk
    • (in Russian). Schor N.Z. Permanents and the problem of planar graphs coloring. Permanents: Theory and Applications (1990), Mezhvuz. Sb., Krasn. Polytechn. Inst., Krasnoyarsk 135-138
    • (1990) Permanents: Theory and Applications , pp. 135-138
    • Schor, N.Z.1
  • 187
    • 0040916017 scopus 로고
    • On lower bounds for permanents
    • (= Indag. Math. 42)
    • (= Indag. Math. 42). Schrijver A., and Valiant W.G. On lower bounds for permanents. Proc. Kon. Ned. Akad. Wet. A 83 (1980) 425-427
    • (1980) Proc. Kon. Ned. Akad. Wet. A , vol.83 , pp. 425-427
    • Schrijver, A.1    Valiant, W.G.2
  • 188
    • 11544311158 scopus 로고
    • On the number of edge colourings of regular bipartite graphs
    • Schrijver A. On the number of edge colourings of regular bipartite graphs. Discrete Math. 38 (1982) 297-301
    • (1982) Discrete Math. , vol.38 , pp. 297-301
    • Schrijver, A.1
  • 189
    • 10044294446 scopus 로고
    • Bounds on permanents and the number of 1-factors and 1-factorizations of bipartite graphs
    • Schrijver A. Bounds on permanents and the number of 1-factors and 1-factorizations of bipartite graphs. London Math. Soc. Lect. Note Ser. vol. 82 (1983) 107-134
    • (1983) London Math. Soc. Lect. Note Ser. , vol.82 , pp. 107-134
    • Schrijver, A.1
  • 190
    • 0000374635 scopus 로고
    • :Uber endliche Gruppen und Hermitische Formen
    • Schur I. :Uber endliche Gruppen und Hermitische Formen. Math. Z. 1 (1918) 184-207
    • (1918) Math. Z. , vol.1 , pp. 184-207
    • Schur, I.1
  • 191
    • 0041835144 scopus 로고
    • The number of edge 3-colorings of a planar cubic graph as a permanent
    • Sheim D.E. The number of edge 3-colorings of a planar cubic graph as a permanent. Discrete Math 8 (1974) 377-382
    • (1974) Discrete Math , vol.8 , pp. 377-382
    • Sheim, D.E.1
  • 192
    • 34648862482 scopus 로고
    • A problem related to the van der Waerden permanent theorem
    • Sinkhorn R. A problem related to the van der Waerden permanent theorem. Linear and Multilinear Algebra 16 (1984) 167-173
    • (1984) Linear and Multilinear Algebra , vol.16 , pp. 167-173
    • Sinkhorn, R.1
  • 193
    • 34250156445 scopus 로고
    • Normal subgroups of complete linear group degree 3 over distributive structure
    • (in Russian)
    • (in Russian). Skornjakov L.A., and Egorova D.P. Normal subgroups of complete linear group degree 3 over distributive structure. Algebra i Logika 23 (1984) 670-683
    • (1984) Algebra i Logika , vol.23 , pp. 670-683
    • Skornjakov, L.A.1    Egorova, D.P.2
  • 194
    • 0039579463 scopus 로고
    • Minimum permanents of certain faces of matrices containing an identity submatrix
    • Song S.-Z. Minimum permanents of certain faces of matrices containing an identity submatrix. Linear Algebra Appl. 108 (1988) 263-280
    • (1988) Linear Algebra Appl. , vol.108 , pp. 263-280
    • Song, S.-Z.1
  • 195
    • 0000194752 scopus 로고
    • The number of faces of a simplicial convex polytope
    • Stanley R. The number of faces of a simplicial convex polytope. Adv. Math. 35 (1980) 236-238
    • (1980) Adv. Math. , vol.35 , pp. 236-238
    • Stanley, R.1
  • 196
    • 0002876380 scopus 로고
    • Two combinatorial applications of the Alexandrov-Fenchel inequalities
    • Stanley R. Two combinatorial applications of the Alexandrov-Fenchel inequalities. J. Combin. Theory Ser. A 31 (1981) 56-65
    • (1981) J. Combin. Theory Ser. A , vol.31 , pp. 56-65
    • Stanley, R.1
  • 197
    • 70350098557 scopus 로고
    • Permanent polynomials and their application in graph theory
    • (in Russian), Mezhvuz. Sb., Krasn. Polytechn. Inst, Krasnoyarsk
    • (in Russian). Strok V.V. Permanent polynomials and their application in graph theory. Permanent: Theory and Applications (1990), Mezhvuz. Sb., Krasn. Polytechn. Inst, Krasnoyarsk
    • (1990) Permanent: Theory and Applications
    • Strok, V.V.1
  • 198
    • 0040185084 scopus 로고
    • Du Theoreme de l'Index de Hodge aux inègalites isoperimetriques
    • Teissier B. Du Theoreme de l'Index de Hodge aux inègalites isoperimetriques. C. R. Acad. Sci. Paris 288 (1979) 287-289
    • (1979) C. R. Acad. Sci. Paris , vol.288 , pp. 287-289
    • Teissier, B.1
  • 199
    • 41949114177 scopus 로고
    • Bonnesen-type inequalities in algebraic geometry, I. Introduction to the problem
    • Princeton, NJ
    • Teissier B. Bonnesen-type inequalities in algebraic geometry, I. Introduction to the problem. Proceedings, Seminar of Differential Geometry. Princeton, NJ (1982) 85-105
    • (1982) Proceedings, Seminar of Differential Geometry , pp. 85-105
    • Teissier, B.1
  • 201
    • 0041874213 scopus 로고
    • On the permanent of a bistochastic matrix
    • Tverberg H. On the permanent of a bistochastic matrix. Math. Scand. 12 (1963) 25-35
    • (1963) Math. Scand. , vol.12 , pp. 25-35
    • Tverberg, H.1
  • 202
    • 49249151236 scopus 로고
    • The complexity of computing the permanent
    • Valiant L.G. The complexity of computing the permanent. Theor. Comput. Sci. 8 (1979) 181-201
    • (1979) Theor. Comput. Sci. , vol.8 , pp. 181-201
    • Valiant, L.G.1
  • 203
    • 0346497653 scopus 로고
    • A lower bound for the permanents of certain (0, 1)-matrices
    • (= Indag. Math. 41)
    • (= Indag. Math. 41). Voorhoeve M. A lower bound for the permanents of certain (0, 1)-matrices. Proc. Kon. Ned. Akad. Wet. A 82 (1979) 83-86
    • (1979) Proc. Kon. Ned. Akad. Wet. A , vol.82 , pp. 83-86
    • Voorhoeve, M.1
  • 205
    • 70350099805 scopus 로고
    • Ein Satz über Klasseneinteilungen von endlichen Mengen
    • Waerden v.d.B.L. Ein Satz über Klasseneinteilungen von endlichen Mengen. Abh. a.d. Math. Seminar Hamburg 5 (1927) 185-188
    • (1927) Abh. a.d. Math. Seminar Hamburg , vol.5 , pp. 185-188
    • Waerden, v.d.B.L.1
  • 207
    • 58149413828 scopus 로고
    • A mechanical counting method and combinatorial applications
    • Wilf H.S. A mechanical counting method and combinatorial applications. J. Combin. Theory 4 (1968) 246-258
    • (1968) J. Combin. Theory , vol.4 , pp. 246-258
    • Wilf, H.S.1
  • 208
    • 0040221600 scopus 로고
    • Nonisomorphic Steiner triple systems
    • Wilson R.M. Nonisomorphic Steiner triple systems. Math. Z. 135 (1974) 303-313
    • (1974) Math. Z. , vol.135 , pp. 303-313
    • Wilson, R.M.1
  • 209
    • 0039145872 scopus 로고
    • On the asymptotic number of Latin rectangles
    • Yamamoto K. On the asymptotic number of Latin rectangles. Japan J. Math. 21 (1951) 113-119
    • (1951) Japan J. Math. , vol.21 , pp. 113-119
    • Yamamoto, K.1
  • 210
    • 0040852943 scopus 로고
    • Structure polynomials of Latin rectangles and its application to a combinatorial problem
    • Yamamoto K. Structure polynomials of Latin rectangles and its application to a combinatorial problem. Mem. Fac. Sci. Kyushu Univ. A. 10 (1956) 1-13
    • (1956) Mem. Fac. Sci. Kyushu Univ. A. , vol.10 , pp. 1-13
    • Yamamoto, K.1


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