J Austral Math Soc Ser A 55 pp411--413, 1993.

A Note of the Union-Closed Sets Conjecture

R. M. Norton and D. G. Sarvate

(Received 28 March 1991; revised 30 September 1991)

Abstract

Let A = {A₁, ..., A_n} be a union-closed set. This note establishes a property which which must be possessed by any smallest counterexample to the conjecture with minimal n has at least three distinct elements, each of which appears in exactly (n - 1)/2 of the A'_js.

1991 AMS Subject Classification: 05A99

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Authors

R. M. Norton: College of Charleston, Charleston, SC 29424, USA.
D. G. Sarvate: College of Charleston, Charleston, SC 29424, USA.

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Last Modified: Fri Jan 10 8:53:39 2003