✦ LIBER ✦

Another Simple Proof of a Theorem of Milner

✍ Scribed by A.D Scott

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 74 KB
Volume: 87
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2956

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✦ Synopsis

In this note we give a short proof of a theorem of Milner concerning intersecting Sperner systems.

1999 Academic Press

An intersecting Sperner system on [n]=[1, ..., n] is a collection of subsets of [n], no pair of which is either disjoint or nested. Milner [2] proved that an intersecting Sperner system on [n] has at most \ n W(n+1)Â2X+ sets. Katona [1] gave a simple proof of Milner's theorem using the cycle method. We give a simpler proof that uses the cycle method in a different way.
We write [n] (k) for the set of subsets of size k of
By a simple counting argument, if knÂ2 then | & F| |F|.

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