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Coxeter cones and their h-vectorsAlgebra & Discrete Mathematics
|Speaker: ||John Stembridge, U. Michigan|
|Location: ||2112 MSB|
|Start time: ||Fri, May 2 2008, 1:10PM|
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.