The University of Michigan Combinatorics Seminar


Abstract 

The higher Bruhat orders are a generalization of the weak Bruhat order on S_{n}. They can be defined combinatorially in terms of inversion sets, generalizing the notion of inversion set of a permutation, or geometically as sets of dfaces of an ncube, generalizing the description of S_{n} as paths through an ncube. The higher StasheffTamari posets (which generalize the Tamari lattices) have an analogous geometric definition where the cube is replaced by a simplex. In this talk, I will review all the necessary definitions, and then discuss a new combinatorial "inversion set" description of the higher StasheffTamari posets which amounts to giving an embedding from each StasheffTamari poset into a corresponding higher Bruhat order. 