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

W. E. Longstaff

doi:10.1017/S1446788700018899

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

Published online by Cambridge University Press: 09 April 2009

W. E. Longstaff

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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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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.