Determinants of matrices of conference type

F.C. Bussemaker, I. Kaplansky, B. McKay, J.J. Seidel

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2 Citations (Scopus)

Abstract

An n by n conference type matrix has 0's on the main diagonal and ±1's elsewhere. We investigate the largest possible determinant of such a matrix. The literature is extensive for n even, but for n odd the question has not been previously studied. We determine the maxima up to n = 11: for n = 3, 5, 7, 9, 11 they are 2, 22, 394, 8760, 240786. It will require a new idea or a huge computation to go beyond n = 11.
Original languageEnglish
Pages (from-to)275-292
JournalLinear Algebra and Its Applications
Volume261
Issue number1-3
DOIs
Publication statusPublished - 1997

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Bussemaker, F.C. ; Kaplansky, I. ; McKay, B. ; Seidel, J.J. / Determinants of matrices of conference type. In: Linear Algebra and Its Applications. 1997 ; Vol. 261, No. 1-3. pp. 275-292.
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Determinants of matrices of conference type. / Bussemaker, F.C.; Kaplansky, I.; McKay, B.; Seidel, J.J.

In: Linear Algebra and Its Applications, Vol. 261, No. 1-3, 1997, p. 275-292.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Bussemaker, F.C.

AU - Kaplansky, I.

AU - McKay, B.

AU - Seidel, J.J.

PY - 1997

Y1 - 1997

N2 - An n by n conference type matrix has 0's on the main diagonal and ±1's elsewhere. We investigate the largest possible determinant of such a matrix. The literature is extensive for n even, but for n odd the question has not been previously studied. We determine the maxima up to n = 11: for n = 3, 5, 7, 9, 11 they are 2, 22, 394, 8760, 240786. It will require a new idea or a huge computation to go beyond n = 11.

AB - An n by n conference type matrix has 0's on the main diagonal and ±1's elsewhere. We investigate the largest possible determinant of such a matrix. The literature is extensive for n even, but for n odd the question has not been previously studied. We determine the maxima up to n = 11: for n = 3, 5, 7, 9, 11 they are 2, 22, 394, 8760, 240786. It will require a new idea or a huge computation to go beyond n = 11.

U2 - 10.1016/S0024-3795(96)00412-0

DO - 10.1016/S0024-3795(96)00412-0

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EP - 292

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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