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

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Abstract

Let g(n, m) denote the maximal number of distinct rows in any (0, l)-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 2* vectors all of whose coordinates are 0 or 1.

Original languageEnglish (US)
Pages (from-to)193-201
Number of pages9
JournalJournal of the Australian Mathematical Society
Volume31
Issue number2
DOIs
StatePublished - Aug 1981

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