The $γ$-vector of a barycentric subdivision
Eran Nevo, T. Kyle Petersen, Bridget Eileen Tenner · arXiv (Cornell University) · 2010
We prove that the $γ$-vector of the barycentric subdivision of a simplicial sphere is the $f$-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the $h$-vector of the barycentric subdivision of a boolean complex.