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On the ranks of some (0, 1)-matrices with constant row sums

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

A. M. Odlyzko
A. M. Odlyzko
Affiliation:
Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A.
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Abstract

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Let g(n, m) denote the maximal number of distinct rows in any (0, 1 )-matrix with n columns, rank < n, – 1, and all row sums equal to m. This paper determines g(n, m) in all cases:

In addition, it is shown that if V is a k-dimensional vector subspace of any vector space, then V contains at most 2k vectors all of whose coordinates are 0 or 1.

MSC classification

Secondary: 05B20: Matrices (incidence, Hadamard, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 2 , August 1981 , pp. 193 - 201
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Longstaff, W. E., “Combinatorial solution of certain systems of linear equations involving (0, 1) matrices’, J. Austral. Math. Soc. Ser. A 23, (1977), 266–274.CrossRefGoogle Scholar