Matroids, Antimatroids, and the External OrderAlgebra & Discrete Mathematics
|Bryan Gillespie, UC Berkeley
|Mon, Nov 20 2017, 4:15PM
Las Vergnas's active orders are a collection of posets formed from the bases of a matroid using the classical notion of matroid activity. We will describe a remarkable generalization of the external order which endows the independence complex of a matroid with the structure of an antimatroid, a type of greedoid related to abstract convexity theory. The resulting poset is an EL-shellable refinement of the geometric lattice of flats and exhibits a beautiful interplay between matroid theory and lattice theory. Time permitting, we will characterize such "matroidal join-distributive lattices" among all antimatroids.