Jinyoung Park, Rutgers University

Abstract

Counting the number of antichains in the Boolean algebra is known as Dedekind's problem and the asymptotic of this number is known. In this talk I will discuss the number of maximal antichains in the Boolean algebra and the number of maximal independent sets in the hypercube. We will see the asymptotics for the logarithm of these numbers and how they are closely related to the size of the maximum induced matchings. This talk is based on the paper of Ilinca-Kahn with the same title.