Cubical realizations of flag nestohedra and Gal's conjecture

Abstract

We study nestohedra $P_B$ corresponding to building sets $B$. It is shown that every flag nestohedron can be obtained from a cube by successive shavings faces of codimension 2. We receive new Delzant geometric realization of flag nestohedra. The main result of the paper is that Gal's conjecture holds for every flag nestohedron. Moreover, we get the exact estimation of $\gamma$-vectors of $n$-dimensional flag nestohedra: $0\le {\gamma }_i(P_B)\le {\gamma }_i(P{e}^n)$.

9 pages, 1 figure

References in corpus (4)

• Real Root Conjecture fails for five and higher dimensional spheres
• Permutohedra, associahedra, and beyond
• Nested complexes and their polyhedral realizations
• Generating Functions of Nestohedra and Applications

Cited by in corpus (1)

• Upper and lower bound theorems for graph-associahedra