A NOTE OF THE UNION-CLOSED SETS CONJECTURE

Authors
NORTON RM SARVATE DG
Citation
Rm. Norton et Dg. Sarvate, A NOTE OF THE UNION-CLOSED SETS CONJECTURE, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 55, 1993, pp. 411-413
Citations number
6
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
55
Year of publication
1993
Part
3
Pages
411 - 413
Database
ISI
SICI code
0263-6115(1993)55:<411:ANOTUS>2.0.ZU;2-D
Abstract
Let A = (A1,...,A(n)) be a union-closed set. This note establishes a p roperty which must be possessed by any smallest counterexample to the Union-Closed Sets Conjecture. Specifically, a counterexample to the co njecture with minimal n has at least three distinct elements, each of which appears in exactly (n - 1)/2 of the A(j)'s.