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A note of the union-closed sets conjecture

Published:1993-12 Issue:3 Volume:55 Page:411-413
ISSN:0263-6115
Container-title:Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
language:en
Short-container-title:J Aust Math Soc A

Author:

Norton R. M.,Sarvate D. G.

Abstract

AbstractLet = {A1, …, An} be a union-closed set. This note establishes a property which must be possessed by any smallest counterexample to the Union-Closed Sets Conjecture. Specifically, a counterexample to the conjecture with minimal n has at least three distinct elements, each of which appears in exactly (n − 1)/2 of the .

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference6 articles.

1. Enumerative Combinatorics

2. Improved bounds for the union-closed sets conjecture;Sarvate;Ars Combin.,1990

3. On the union-closed sets conjecture;Sarvate;Ars, Combin.,1989

4. A much travelled conjecture;Austral. Math. Soc. Gaz.,1987

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Journey of the Union-Closed Sets Conjecture;Graphs and Combinatorics;2015-01-13

2. Union-closed families of sets;Journal of Combinatorial Theory, Series A;2013-04

3. On averaging Frankl's conjecture for large union-closed-sets;Journal of Combinatorial Theory, Series A;2009-04

4. On the Scope of Averaging for Frankl’s Conjecture;Order;2009-01-17

5. An attempt at frankl’s conjecture;Publications de l'Institut Math?matique (Belgrade);2007

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