6 problems

Let $V$ be an $n$-element set, let $2^V$ denote the simplex on $V$, and let $\Gamma$ be a flag triangulation of $2^V$. Let $ell_V(\Gamma,x)$ denote its local $h$-polynomial. Athanas…

Let $V$ be a $d$-element set, and let $\Gamma$ be a flag vertex-induced homology subdivision of the simplex $2^V$. The local $h$-polynomial has a unique expansion … and…

Athanasia's conjecture. One has

Let $V$ be the vertex set of a simplex $2^V$, and let $\Gamma$ be a flag vertex-induced homology subdivision of $2^V$. Let $\xi_V(\Gamma)$ denote the local $\gamma$-vector associat…

Let $\Delta$ be a flag homology sphere, and let $\Delta'$ be a flag vertex-induced homology subdivision of $\Delta$. Let $\gamma(\Delta)$ and $\gamma(\Delta')$ denote their…

Let $\Delta$ and $\Delta'$ be flag homology spheres, and suppose that $\Delta'$ geometrically subdivides $\Delta$. Let $\gamma(\Delta)$ and $\gamma(\Delta')$ denote their $\gamma$-…