Jinyoung Park, Rutgers University

Abstract

Let Q_n be the n-dimensional Hamming cube (hypercube) and N = 2^n . We prove that the number of maximal independent sets in Q_n is asymptotically 2n2^(N/4), as was conjectured by Ilinca and Kahn in connection with a question of Duffus, Frankl and Rödl. The value is a natural lower bound derived from a connection between maximal independent sets and induced matchings. The proof of the upper bound draws on various tools, among them “stability” results for maximal independent set counts and old and new results on isoperimetric behavior in Q_n. This is joint with Jeff Kahn.