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Maximal Determinants In Combinatorial Investigations

Published online by Cambridge University Press:  20 November 2018

H. J. Ryser
H. J. Ryser*
Affiliation:
Ohio State University
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1. Introduction. Let Q be a matrix of order v, all of whose entries are 0's and l's. Let the total number of l's in Q be t, and let the absolute value of the determinant of Q be denoted by |det Q|. In this paper we study the problem of determining the maximum of |det Q| for fixed t and v. It turns out that this problem is closely related to the v, k, λ problem, which has been extensively studied of late.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 245 - 249
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Bruck, R. H. and Ryser, H. J., The nonexistence of certain finite projective planes, Can. J. Math., 1 (1949), 88–93.Google Scholar
2. Chowla, S. and Ryser, H. J., Combinatorial problems, Can. J. Math., 2 (1950), 93–99.Google Scholar
3. Paley, R. E. A. C., On orthogonal matrices, J. Math. Phys., 12 (1933), 311–320.Google Scholar
4. Ryser, H. J., Geometries and incidence matrices, Slaught Memorial Papers (Suppl. Amer. Math. Monthly), 62 (1955), 25–31.Google Scholar
5. Williamson, John, Determinants whose elements are 0 and 1, Amer. Math. Monthly, 53 (1946), 427–434.Google Scholar