Large families of subsets avoiding a given configuration

Jerrold R. Griggs

University of South Carolina, Columbia, SC

Abstract

Translating Tur\'an-type questions to ordered sets, we are interested in the maximum size La(n,H) of a family F of subsets of the set {1,2,...,n}, subject to the condition that a certain configuration (subposet H) is excluded.

For instance, Sperner's Theorem solves the problem for H being a two-element chain. We survey results of this kind, including bounds when H is the four-element N poset (joint with Gyula O.H. Katona) or a more general height two poset (joint with Linyuan Lincoln Lu).