Speaker: Ramon Garcia (UIUC)
Title: Maximal independent sets in the middle two layers of the Boolean lattice
Abstract: Let B(2d − 1, d) be the subgraph of the Boolean lattice Q_(2d−1) induced by the two largest layers. Duffus, Frankl and Rödl proposed the problem of finding the asymptotics for the logarithm of the number of maximal independent sets in B(2d-1, d). Ilinca and Kahn determined the logarithmic asymptotics and raised the question of what their order of magnitude is. In this talk, we provide precise asymptotics for the number of maximal independent sets in B(2d-1,d) and describe their typical structure. This is ongoing research in collaboration with József Balogh and Ce Chen.