Algebraic Combinatorics Seminar - Christos Athanasiadis

Title: Face enumeration and real-rootedness

Abstract:

About fifteen years ago F. Brenti and V. Welker showed that the face enumerating polynomial of the barycentric subdivision of any Cohen-Macaulay simplicial complex has only real roots. It is natural to ask whether similar results hold when barycentric subdivision is replaced by more general types of triangulations, or when simplicial complexes are replaced by more general cell complexes. This talk will report on recent progress on these questions. For various special types of triangulations, there are strong connections to traditional combinatorial themes, such as the enumeration of permutations, words, signed permutations and ordered set partitions.