For any flag simplicial complex $\Theta$ obtained by stellar subdividing the boundary of the cross polytope in edges, we define a flag simplicial complex $\Delta(\Theta)$ whose $f$-vector is the $\gamma$-vector of $\Theta$. This proves that the $\gamma$-vector of any such simplicial complex is the face vector of a flag simplicial complex, partially solving a conjecture by Nevo and Petersen. As a corollary we obtain that such simplicial complexes satisfy the Frankl-Füredi-Kalai inequalities.
@article{10_37236_9301,
author = {Natalie Aisbett and Vadim Volodin},
title = {Geometric realization of \(\gamma \)-vectors of subdivided cross polytopes},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {2},
doi = {10.37236/9301},
zbl = {1441.05250},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9301/}
}
TY - JOUR
AU - Natalie Aisbett
AU - Vadim Volodin
TI - Geometric realization of \(\gamma \)-vectors of subdivided cross polytopes
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9301/
DO - 10.37236/9301
ID - 10_37236_9301
ER -
%0 Journal Article
%A Natalie Aisbett
%A Vadim Volodin
%T Geometric realization of \(\gamma \)-vectors of subdivided cross polytopes
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9301/
%R 10.37236/9301
%F 10_37236_9301
Natalie Aisbett; Vadim Volodin. Geometric realization of \(\gamma \)-vectors of subdivided cross polytopes. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/9301
