Combinatorics Seminar - William Gustafson
Speaker: William Gustafson
Title: Lattice minors and Eulerian posets
Abstract: We introduce a notion of deletion and contraction on lattices enriched with a generating set, and from these operations a notion of minors. When considering the lattice of flats of a graph the lattice minors are in bijection with the simple minors of the graph when the vertices are labeled and the edges are unlabeled. We show how this correspondence generalizes to the setting of polymatroids. Then we introduce the minor poset of a given generator enriched lattice and show these posets are Eulerian and PL spheres. Finally we discuss some inequalities between the cd-indices of minor posets.