The higher Stasheff-Tamari posets and the higher Bruhat orders

Hugh Thomas

Fields Institute, University of Toronto

October 16,
refreshments at 3:45pm


The higher Bruhat orders are a generalization of 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 d-faces of an n-cube, generalizing the description of S_n as paths through an n-cube. The higher Stasheff-Tamari 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 Stasheff-Tamari posets which amounts to giving from each Stasheff-Tamari poset into a corresponding higher Bruhat order.

Speaker's Contact Info: hthomas(at-sign)

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