MATH Seminar

Title: Set families with a forbidden induced subposet
Seminar: Combinatorics
Speaker: Tao Jiang of Miami university
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2013-11-15 at 4:00PM
Venue: W306
Download Flyer
Abstract: Sperner’s theorem asserts that the largest antichain in a Boolean lattice Bn has size n n/2 . A few years ago, Bukh obtained a substantial asymptotic extension of Sperner’s theorem by proving that for any poset H whose Hasse diagram is a tree of height k, the largest size of a n subfamily of Bn not containing H is asymptotic to (k − 1) n/2 . We establish an induced version of Bukh’s result, namely that the largest size of a subfamily of Bn not containing H as an induced n subposet, is also asymptotic to (k −1) n/2 . This is an old result (2012). I will focus on presenting the ideas of the proof. This is joint work with Ed Boenhlein.