Combinatorics Seminar

Given a graph G on n vertices, Postnikov defined a graph associahedron P_G as an example of a generalized permutohedron, a polytope whose normal fan coarsens the braid arrangement. Combinatorially, each face of P_G corresponds to certain collections of compatible subgraphs of G called tubings. Graph associahedra were introduced independently by Carr and Devadoss and by Davis, Januszkiewicz, and Scott. In this talk, we consider the poset obtained by orienting the one-skeleton of P_G according to a certain linear functional, and its relationship to the weak order on S_n.
Speaker(s): Emily Barnard (De Paul University)