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Combinatorial solution of certain systems of linear equations involving (0,1) matrices

Published online by Cambridge University Press:  09 April 2009

W. E. Longstaff
W. E. Longstaff
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, W.A., 6009, Australia.
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Abstract

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If m and n are natural numbers satisfying 1 ≦ m < n let denote the least integer k such that the statement: ‘Every (0,1) matrix with n columns, with constant row-sum m, and with at least k distinct rows, has rank n’ is true. Then = +1 for m ≧ 2, n ≧ m2 + 2. Further, for 1 ≦ m < n.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 266 - 274
Copyright
Copyright © Australian Mathematical Society 1977