Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-25T04:02:42.905Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]‘A much-travelled conjecture’, Austral. Math. Soc. Gaz. 14 (3) (1987), 63.Google Scholar
[2]Norton, R. M. and Sarvate, D. G., ‘Union-closed sets conjecture: some observations’, (manuscript, College of Charleston, 09 1989).Google Scholar
[3]Sarvate, D. G. and Renaud, J-C., ‘On the union-closed sets conjecture’, Ars Combin. 27 (1989), 149–154.Google Scholar
[4]Sarvate, D. G. ‘Improved bounds for the union-closed sets conjecture’, Ars Combin. 29 (1990), 181–185.Google Scholar
[5]Winkler, P., ‘Union-closed sets conjecture’, Austral. Math. Soc. Gaz. 14 (4) (1987), 99.Google Scholar