Local $h$-vectors of Quasi-Geometric and Barycentric Subdivisions

Martina Juhnke-Kubitzke, Satoshi Murai, Richard Sieg

Published 2017-04-26Version 1

In this paper, we answer two questions on local $h$-vectors, which were asked by Athanasiadis. First, we characterize all possible local $h$-vectors of quasi-geometric subdivisions of a simplex. Second, we prove that the local $\gamma$-vector of the barycentric subdivision of any CW-regular subdivision of a simplex is nonnegative. Along the way, we derive a new recurrence formula for the derangement polynomials.