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Volumn 257, Issue 1-3, 1997, Pages 289-306

The maximum determinant of ± 1 matrices

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EID: 0000363833     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00147-4     Document Type: Article
Times cited : (28)

References (28)
  • 1
    • 0005589789 scopus 로고
    • Hadamard matrices and their application
    • Springer-Verlag, Berlin
    • S. S. Agaian, Hadamard Matrices and Their Application, Lecture Notes in Math. 1168, Springer-Verlag, Berlin, 1985.
    • (1985) Lecture Notes in Math , pp. 1168
    • Agaian, S.S.1
  • 2
    • 0003226860 scopus 로고
    • Designs and their codes
    • Cambridge U.P., Cambridge
    • E. F. Assmus, Jr., and J. D. Key, Designs and Their Codes, Cambridge Tracts in Math. 103, Cambridge U.P., Cambridge, 1992.
    • (1992) Cambridge Tracts in Math , pp. 103
    • Assmus E.F., Jr.1    Key, J.D.2
  • 3
    • 0009107643 scopus 로고
    • Intorno al teorema di Hadamard sui determinanti a valore massimo
    • G. Barba, Intorno al teorema di Hadamard sui determinanti a valore massimo, Giorn. Mat. Battaglia 71:70-86 (1933).
    • (1933) Giorn. Mat. Battaglia , vol.71 , pp. 70-86
    • Barba, G.1
  • 5
    • 0005965402 scopus 로고
    • The Hadamard maximum determinant problem
    • J. Brenner, The Hadamard maximum determinant problem, Amer. Math. Monthly 79:626-629 (1972).
    • (1972) Amer. Math. Monthly , vol.79 , pp. 626-629
    • Brenner, J.1
  • 8
    • 38149144751 scopus 로고
    • The maximum determinant of 21 × 21 (± 1, -1)-matrices and D-optimal designs
    • T. Chadjipantelis, C. Moyssiadis, and S. Kounias, The maximum determinant of 21 × 21 (± 1, -1)-matrices and D-optimal designs, J. Statist. Plann. Inference 16:167-178 (1987).
    • (1987) J. Statist. Plann. Inference , vol.16 , pp. 167-178
    • Chadjipantelis, T.1    Moyssiadis, C.2    Kounias, S.3
  • 9
    • 84966234878 scopus 로고
    • A sequence of (± 1)-determinants with large values
    • G. F. Clements and B. Lindstrom, A sequence of (± 1)-determinants with large values, Proc. Amer. Math. Soc. 16:548-550 (1965).
    • (1965) Proc. Amer. Math. Soc. , vol.16 , pp. 548-550
    • Clements, G.F.1    Lindstrom, B.2
  • 10
    • 0039123393 scopus 로고
    • Sui valore missimi dei determinanti ad elementi + 1 e - 1
    • A. Colucci, Sui valore missimi dei determinanti ad elementi + 1 e - 1, Giorn. Mat. Battaglini 64:217-221 (1926).
    • (1926) Giorn. Mat. Battaglini , vol.64 , pp. 217-221
    • Colucci, A.1
  • 11
    • 84962991807 scopus 로고
    • Determinants with elements ± 1
    • J. H. E. Cohn, Determinants with elements ± 1, J. London Math. Soc. 42:436-442 (1967).
    • (1967) J. London Math. Soc. , vol.42 , pp. 436-442
    • Cohn, J.H.E.1
  • 12
    • 0003117604 scopus 로고
    • On determinants with elements ± 1, II
    • J. H. E. Cohn, On determinants with elements ± 1, II, Bull. London Math. Soc. 21:36-42 (1989).
    • (1989) Bull. London Math. Soc. , vol.21 , pp. 36-42
    • Cohn, J.H.E.1
  • 13
    • 0001767925 scopus 로고
    • Determinantenabschätzungen für binäre matrizen
    • H. Ehlich, Determinantenabschätzungen für binäre Matrizen, Math. Z. 83:123-132 (1964).
    • (1964) Math. Z. , vol.83 , pp. 123-132
    • Ehlich, H.1
  • 14
    • 0002304176 scopus 로고
    • Determinantenabschätzungen für binäre matrizen mit n ≡ 3 (mod 4)
    • H. Ehlich, Determinantenabschätzungen für binäre Matrizen mit n ≡ 3 (mod 4), Math. Z. 84:438-477 (1964).
    • (1964) Math. Z. , vol.84 , pp. 438-477
    • Ehlich, H.1
  • 15
    • 0001206398 scopus 로고
    • D-optimum weighing designs
    • Z. Galil and J. Kiefer, D-optimum weighing designs, Ann. Statist. 8(6): 1293-1306 (1980).
    • (1980) Ann. Statist. , vol.8 , Issue.6 , pp. 1293-1306
    • Galil, Z.1    Kiefer, J.2
  • 16
    • 0000720098 scopus 로고
    • Résolution d'une question relative aux déterminants
    • J. Hadamard, Résolution d'une question relative aux déterminants, Bull. Sci. Math. 2:240-246 (1893).
    • (1893) Bull. Sci. Math. , vol.2 , pp. 240-246
    • Hadamard, J.1
  • 18
    • 0039123390 scopus 로고    scopus 로고
    • private communication
    • I. Kaplansky, private communication.
    • Kaplansky, I.1
  • 19
    • 0002355370 scopus 로고
    • Supplementary difference sets and optimal designs
    • C. Koukouvinos, S. Kounias, and J. Seberry, Supplementary difference sets and optimal designs, Discrete Math. 88:49-58 (1991).
    • (1991) Discrete Math. , vol.88 , pp. 49-58
    • Koukouvinos, C.1    Kounias, S.2    Seberry, J.3
  • 21
    • 0003019045 scopus 로고
    • The exact D-optimal first order saturated design with 17 observations
    • C. Moyssiadis and S. Kounias, The exact D-optimal first order saturated design with 17 observations, J. Statist. Plann. Inference 7:13-27 (1982).
    • (1982) J. Statist. Plann. Inference , vol.7 , pp. 13-27
    • Moyssiadis, C.1    Kounias, S.2
  • 22
    • 0039123387 scopus 로고
    • Remarques sur le maximum d'un déterminant dont torus les éléments sont non-négatifs
    • T. Popoviciu, Remarques sur le maximum d'un déterminant dont torus les éléments sont non-négatifs, Soc. Sci. Cluj 8:572-582 (1937).
    • (1937) Soc. Sci. Cluj , vol.8 , pp. 572-582
    • Popoviciu, T.1
  • 23
    • 0039715628 scopus 로고    scopus 로고
    • private communication
    • B. Solomon, private communication.
    • Solomon, B.1
  • 24
    • 0003330080 scopus 로고
    • Theory of Optimal Designs
    • Springer-Verlag
    • K. Shah and B. Sinha, Theory of Optimal Designs, Lecture Notes in Statist. 54, Springer-Verlag, 1989.
    • (1989) Lecture Notes in Statist , vol.54
    • Shah, K.1    Sinha, B.2
  • 26
    • 0001762205 scopus 로고
    • Thoughts on inverse orthogonal matrices, simultaneous signsuccession, and tesselated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers
    • J. J. Sylvester, Thoughts on inverse orthogonal matrices, simultaneous signsuccession, and tesselated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers, London Edinburgh and Dublin Philos. Mag. and J. Sci. 34:461-475 (1867).
    • (1867) London Edinburgh and Dublin Philos. Mag. and J. Sci. , vol.34 , pp. 461-475
    • Sylvester, J.J.1
  • 27
    • 0002046445 scopus 로고
    • A family of D-optimal designs
    • A. Whiteman, A family of D-optimal designs, Ars Combin. 30:23-26 (1990).
    • (1990) Ars Combin. , vol.30 , pp. 23-26
    • Whiteman, A.1
  • 28
    • 0002115665 scopus 로고
    • On Hadamard's inequality for the determinants of order non-divisible by 4
    • M. Mojtas, On Hadamard's inequality for the determinants of order non-divisible by 4, Colloq. Math. 12:73-83 (1964).
    • (1964) Colloq. Math. , vol.12 , pp. 73-83
    • Mojtas, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.