✦ LIBER ✦

On the structure of maximum 2-part Sperner families

✍ Scribed by Shahriar Shahriari

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 479 KB
Volume: 162
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00288-8

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✦ Synopsis

Color the elements of a finite set S with two colors. A collection of subsets of S is called a 2-part Sperner family if whenever for two distinct sets A and B in this collection we have A c B then B -A has elements of S of both colors. All 2-part Sperner families of maximum size were characterized in Erd6s and Katona (1986). In this paper we provide a different, and quite elementary proof of the structure and number of all maximum 2-part Sperner families, using only some elementary properties of symmetric chain decompositions of the poset of all subsets of a finite set.

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