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.
Bibliographical noteFunding Information:
E-mail addresses: firstname.lastname@example.org (E. Nevo), email@example.com (T.K. Petersen), firstname.lastname@example.org (B.E. Tenner). 1 The author was partially supported by an NSF Award DMS-0757828.
- Charney-Davis conjecture
- Gal's conjecture