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Is the Union-closed sets conjecture the best possible?

Part of: Combinatorics

Published online by Cambridge University Press:  09 April 2009

J. C. Renaud
J. C. Renaud
Affiliation:
Department of Mathematics University of Papua New GuineaP. O. Box 320, University Papua, New Guinea
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Abstract

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A slightly strengthened version of the union-closed sets conjecture is proposed. It is shown that this version holds for a minimum set size of one or two and an examination of a boundary function shows that it holds for collections containing up to 19 sets. Some related conjectures are outlined.

MSC classification

Secondary: 05A15: Exact enumeration problems, generating functions 05A05: Permutations, words, matrices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 2 , October 1991 , pp. 276 - 283
Copyright
Copyright © Australian Mathematical Society 1991

References

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[5]Winkler, P., ‘Union-closed sets conjecture’, Austral. Math. Soc. Gaz. 14 (4) (1987), 99.Google Scholar