Shellability of a Poset of Polygonal Subdivisions

Abstract

We introduce a sequence of posets closely related to the associahedra. In this we are motivated by reasons similar to those of Stasheff in the case of the associahedra. We make a study of this poset showing that it has an inductive structure with proper downwards intervals being products of smaller posets in the same series and associahedra. Using this we also show that they are thin dual CL-shellable and in particular that they are the face poset of a regular cell decomposition of the ball.