Mathematics Colloquia and Seminars

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Abstract: Understanding the h-vectors of various classes of simplicial complexes has been a topic of longstanding interest in topological combinatorics. A particular focus of attention has been the identification of natural conditions that force unimodality of the h-vector. In this talk, we will discuss results of this type for "Coxeter cones". These are simplicial fans formed by intersecting the nonnegative sides of a subset of root hyperplanes in some root system. They are (shellable) subcomplexes of the Coxeter complex, and their h-vectors record the distribution of descents among their chambers. We identify a natural class of "graded" Coxeter cones with the property that their h-vectors are symmetric and unimodal, thereby generalizing recent theorems of Reiner-Welker and Brändén about the Eulerian polynomials of graded partially ordered sets.