메뉴 건너뛰기




Volumn 7, Issue 2, 1997, Pages 181-264

Noncommutative symmetric functions II: Transformations of alphabets

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0031515618     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196797000113     Document Type: Article
Times cited : (104)

References (40)
  • 1
    • 0001190473 scopus 로고
    • Solomon's descent algebra revisited
    • M. D. Atkinson, Solomon's descent algebra revisited, Bull. London Math. Soc. 24 (1992), 545-551.
    • (1992) Bull. London Math. Soc. , vol.24 , pp. 545-551
    • Atkinson, M.D.1
  • 2
    • 0006692025 scopus 로고
    • Idempotents for the free Lie algebra and q-enumeration
    • Invariant theory and tableaux, D. Stanton Ed., Springer
    • F. Bergeron, N. Bergeron and A. M. Garsia, Idempotents for the free Lie algebra and q-enumeration, in Invariant theory and tableaux, D. Stanton Ed., IMA Volumes in Mathematics and its Applications, 19 (Springer, 1988).
    • (1988) IMA Volumes in Mathematics and Its Applications , vol.19
    • Bergeron, F.1    Bergeron, N.2    Garsia, A.M.3
  • 3
    • 0012251579 scopus 로고
    • Homomorphisms between Solomon's descent algebras
    • F. Bergeron, A. Garsia and C. Reutenauer, Homomorphisms between Solomon's descent algebras, J. Algebra 150 (1992), 503-519.
    • (1992) J. Algebra , vol.150 , pp. 503-519
    • Bergeron, F.1    Garsia, A.2    Reutenauer, C.3
  • 4
    • 0039286108 scopus 로고
    • Explicit solution of the continuous Baker-Campbell-Hausdorff problem
    • I. Bialynicki-Birula, B. Mielnik and J. Plebański, Explicit solution of the continuous Baker-Campbell-Hausdorff problem, Annals of Physics 51 (1969), 187-200.
    • (1969) Annals of Physics , vol.51 , pp. 187-200
    • Bialynicki-Birula, I.1    Mielnik, B.2    Plebański, J.3
  • 6
    • 84966214880 scopus 로고
    • Representations of the symmetric group in deformations of the free Lie algebra
    • A. R. Calderbank, P. Hanlon and S. Sundaram, Representations of the symmetric group in deformations of the free Lie algebra, Trans. Amer. Math. Soc. 341 (1994), 315-333.
    • (1994) Trans. Amer. Math. Soc. , vol.341 , pp. 315-333
    • Calderbank, A.R.1    Hanlon, P.2    Sundaram, S.3
  • 7
    • 0026104301 scopus 로고
    • Orthogonal projection onto the free Lie algebra
    • G. Duchamp, Orthogonal projection onto the free Lie algebra, Theor. Comp. Sci. 79 (1991), 227-239.
    • (1991) Theor. Comp. Sci. , vol.79 , pp. 227-239
    • Duchamp, G.1
  • 9
    • 0001204370 scopus 로고
    • Calculation of the coefficients in the Campbell-Baker-Hausdorff formula
    • in Russian
    • E. B. Dynkin, Calculation of the coefficients in the Campbell-Baker-Hausdorff formula, Dokl. Akad. Nauk. SSSR (N.S.) 57 (1947), 323-326 (in Russian).
    • (1947) Dokl. Akad. Nauk. SSSR (N.S.) , vol.57 , pp. 323-326
    • Dynkin, E.B.1
  • 10
    • 0003131433 scopus 로고
    • Combinatorics of the free Lie algebra and the symmetric group
    • Academic press, New York
    • A. M. Garsia, Combinatorics of the free Lie algebra and the symmetric group, in Analysis, et cetera . . . , Jürgen Moser Festschrift (Academic press, New York, 1990), 309-82.
    • (1990) Analysis, et Cetera . . . , Jürgen Moser Festschrift , pp. 309-382
    • Garsia, A.M.1
  • 11
    • 38249024936 scopus 로고
    • A decomposition of Solomon's descent algebra
    • A. M. Garsia and C. Reutenauer, A decomposition of Solomon's descent algebra, Advances in Math. 77 (1989), 189-262.
    • (1989) Advances in Math. , vol.77 , pp. 189-262
    • Garsia, A.M.1    Reutenauer, C.2
  • 13
    • 0002623668 scopus 로고
    • Determinants of matrices over noncommutative rings
    • I. M. Gelfand and V. S. Retakh, Determinants of matrices over noncommutative rings, Funct. Anal. Appl. 25 (1991), 91-102.
    • (1991) Funct. Anal. Appl. , vol.25 , pp. 91-102
    • Gelfand, I.M.1    Retakh, V.S.2
  • 14
    • 34249837410 scopus 로고    scopus 로고
    • A theory of noncommutative determinants and characteristic functions of graphs
    • I. M. Gelfand and V. S. Retakh, A theory of noncommutative determinants and characteristic functions of graphs, Funct. Anal. Appl. 26 (1992), 1-20; Publ. LACIM, UQAM, Montreal 14, 1-26.
    • (1992) Funct. Anal. Appl. , vol.26 , pp. 1-20
    • Gelfand, I.M.1    Retakh, V.S.2
  • 15
    • 34249837410 scopus 로고    scopus 로고
    • UQAM, Montreal
    • I. M. Gelfand and V. S. Retakh, A theory of noncommutative determinants and characteristic functions of graphs, Funct. Anal. Appl. 26 (1992), 1-20; Publ. LACIM, UQAM, Montreal 14, 1-26.
    • Publ. LACIM , vol.14 , pp. 1-26
  • 16
    • 0001436549 scopus 로고
    • Multipartie P-partitions and inner product of skew Schur functions
    • I. Gessel, Multipartie P-partitions and inner product of skew Schur functions, Contemp. Math. 34 (1984), 289-301.
    • (1984) Contemp. Math. , vol.34 , pp. 289-301
    • Gessel, I.1
  • 17
    • 0001347739 scopus 로고
    • Counting permutations with given cycle structure and descent set
    • I. Gessel and C. Reutenauer, Counting permutations with given cycle structure and descent set, J. Comb. Theory A 64 (1993), 189-215.
    • (1993) J. Comb. Theory A , vol.64 , pp. 189-215
    • Gessel, I.1    Reutenauer, C.2
  • 18
    • 25844451511 scopus 로고
    • Lie elements in the tensor algebra
    • A. A. Klyachko, Lie elements in the tensor algebra, Siberian Math. J. 15 (1974), 1296-1304.
    • (1974) Siberian Math. J. , vol.15 , pp. 1296-1304
    • Klyachko, A.A.1
  • 19
    • 21844497633 scopus 로고
    • Minor identities for quasi-determinants and quantum determinants
    • D. Krob and B. Leclerc, Minor identities for quasi-determinants and quantum determinants, Commun. Math. Phys. 169 (1995), 1-23.
    • (1995) Commun. Math. Phys. , vol.169 , pp. 1-23
    • Krob, D.1    Leclerc, B.2
  • 21
    • 0003167194 scopus 로고
    • Opérations sur l'homologie cyclique des algèbres commutatives
    • J. L. Loday, Opérations sur l'homologie cyclique des algèbres commutatives, Invent. Math. 96 (1989), 205-230.
    • (1989) Invent. Math. , vol.96 , pp. 205-230
    • Loday, J.L.1
  • 22
    • 0003556131 scopus 로고
    • Symmetric functions and Hall polynomials
    • Oxford University Press, 2nd Ed.
    • I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Math. Monographs (Oxford University Press, 2nd Ed., 1994).
    • (1994) Oxford Math. Monographs
    • Macdonald, I.G.1
  • 23
    • 0004205061 scopus 로고
    • Cambridge University Press, 1915, 1916; Chelsea reprint
    • P. A. MacMahon, Combinatory analysis (Cambridge University Press, 1915, 1916; Chelsea reprint, 1960).
    • (1960) Combinatory Analysis
    • MacMahon, P.A.1
  • 24
    • 84940252991 scopus 로고
    • On the exponential solution of differential equations for a linear operator
    • W. Magnus, On the exponential solution of differential equations for a linear operator, Comm. Pure Appl. Math. VII (1954), 649-673.
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 649-673
    • Magnus, W.1
  • 25
    • 0000721182 scopus 로고
    • Duality between quasi-symmetric functions and the Solomon descent algebra
    • C. Malvenuto and C. Reutenauer, Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177 (1995), 967-982.
    • (1995) J. Algebra , vol.177 , pp. 967-982
    • Malvenuto, C.1    Reutenauer, C.2
  • 26
    • 0000150705 scopus 로고
    • Combinatorial approach to Baker-Campbell-Hausdorff exponents
    • B. Mielnik and J. Plebański, Combinatorial approach to Baker-Campbell-Hausdorff exponents, Ann. Inst. Henri Poincaré, Section A, XII (1970), 215-254.
    • (1970) Ann. Inst. Henri Poincaré, Section A , vol.12 , pp. 215-254
    • Mielnik, B.1    Plebański, J.2
  • 28
    • 0642285990 scopus 로고
    • Généralisation d'une formule de Solomon relative à l'anneau d'un groupe de Coxeter
    • P. Moszkowski, Généralisation d'une formule de Solomon relative à l'anneau d'un groupe de Coxeter, C.R. Acad. Sci. Paris 309 (1989), 539-541.
    • (1989) C.R. Acad. Sci. Paris , vol.309 , pp. 539-541
    • Moszkowski, P.1
  • 29
    • 0346745459 scopus 로고
    • Construction géométrique des idempotents eulériens. Filtration des groupes de polytopes et des groupes d'homologie de Hochschild
    • F. Patras, Construction géométrique des idempotents eulériens. Filtration des groupes de polytopes et des groupes d'homologie de Hochschild, Bull. Soc. Math. France 119 (1991), 173-198.
    • (1991) Bull. Soc. Math. France , vol.119 , pp. 173-198
    • Patras, F.1
  • 30
    • 0000031333 scopus 로고
    • L'algèbre des descentes d'une bigèbre graduée
    • F. Patras, L'algèbre des descentes d'une bigèbre graduée, J. Algebra 170 (1994), 547-566.
    • (1994) J. Algebra , vol.170 , pp. 547-566
    • Patras, F.1
  • 32
    • 0001622061 scopus 로고
    • A Frobenius formula for the characters of Hecke algebras
    • A. Ram, A Frobenius formula for the characters of Hecke algebras, Invent. Math. 106 (1991), 461-488.
    • (1991) Invent. Math. , vol.106 , pp. 461-488
    • Ram, A.1
  • 33
    • 0009086724 scopus 로고
    • Theorem of Poincaré-Birkhoff-Witt, logarithm and representations of the symmetric group whose order are the Stirling numbers
    • Combinatoire énumérative, Proceedings, Montréal 1985 (G. Labelle and P. Leroux Eds.), Springer
    • C. Reutenauer, Theorem of Poincaré-Birkhoff-Witt, logarithm and representations of the symmetric group whose order are the Stirling numbers, in Combinatoire énumérative, Proceedings, Montréal 1985 (G. Labelle and P. Leroux Eds.), Lecture Notes in Math. 1234 (Springer, 1986), 267-284.
    • (1986) Lecture Notes in Math. , vol.1234 , pp. 267-284
    • Reutenauer, C.1
  • 35
    • 0001313205 scopus 로고
    • A Mackey formula in the group ring of a Coxeter group
    • L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (1976), 255-268.
    • (1976) J. Algebra , vol.41 , pp. 255-268
    • Solomon, L.1
  • 36
    • 0038113120 scopus 로고
    • On the Poincaré-Birkhoff-Witt theorem
    • L. Solomon, On the Poincaré-Birkhoff-Witt theorem, J. Comb. Th. 4 (1968), 363-375.
    • (1968) J. Comb. Th. , vol.4 , pp. 363-375
    • Solomon, L.1
  • 37
    • 0005920195 scopus 로고
    • Die linearen Beziehungen zwischen höheren Kommutatoren
    • W. Specht, Die linearen Beziehungen zwischen höheren Kommutatoren, Math. Zeit. 51 (1948), 367-376.
    • (1948) Math. Zeit. , vol.51 , pp. 367-376
    • Specht, W.1
  • 38
    • 0002392284 scopus 로고    scopus 로고
    • NCSF, a maple package for noncommutative symmetric functions
    • to appear
    • B. C. V. Ung, NCSF, a maple package for noncommutative symmetric functions, Maple Technical Newsletter (1996), to appear.
    • (1996) Maple Technical Newsletter
    • Ung, B.C.V.1
  • 39
    • 0039806720 scopus 로고
    • Über Invarianten in Lieschen Ringen
    • F. Wever, Über Invarianten in Lieschen Ringen, Math. Annalen 120 (1949), 563-580.
    • (1949) Math. Annalen , vol.120 , pp. 563-580
    • Wever, F.1
  • 40
    • 0042638530 scopus 로고
    • Exponential operators and parameter differentiation in Quantum Physics
    • R. M. Wilcox, Exponential operators and parameter differentiation in Quantum Physics, J. Math. Phys. 8 (1967), 962-982.
    • (1967) J. Math. Phys. , vol.8 , pp. 962-982
    • Wilcox, R.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.