### DIMACS - Graduate Student Combinatorics Seminar

Title: Counting Maximal Antichains and Independent Sets

Speaker: **Jinyoung Park**, Rutgers University

Date: Wednesday, March 29, 2017 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

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.

See: http://www.math.rutgers.edu/~ajr224/GCS.html