University of Delaware
Discrete Mathematics Seminar

Extremal families of subsets and the Lubell function
Lincoln Lu
University of South Carolina
Thursday, April 19, 2012
Ewing Hall 336 5.00 - 6.00 pm

Abstract: We are interested in how large a family of subsets of the n-set {1,...,n} there is that avoids certain patterns. The foundational result of this sort, Sperner's Theorem from 1928, solves this problem for families that contain no two-element chains. Here we will present some recent results on extremal families avoiding a given (weak) subposet, such as crowns, diamonds, batons, etc. We also obtained a better bound on extremal families that contain no d-dimensional Boolean algebras, which was previously studied by Gunderson, Rodl, and Sidorenko. The Lubell function turns out to be a very useful tool to attack these extremal set problems.