✦ LIBER ✦

On a Theorem of J. Ossowski

✍ Scribed by Fred Galvin

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 214 KB
Volume: 78
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.2753

No coin nor oath required. For personal study only.

✦ Synopsis

Consider any matrix of zeros and ones with at most n ones in each row and fewer than (k+1) n ones in all. Ossowski showed that, by deleting no more than k columns, one can get a matrix which contains no r_(n&r+1) submatrix of ones for r=1, 2, ..., n. We give a short proof of Ossowski's theorem in the slightly stronger form: any minimal set of columns, whose deletion has the desired effect, has cardinality at most k.

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