Cubical realizations of flag nestohedra and Gal's conjecture

Details Cubical realizations of flag nestohedra and Gal's conjecture Cubical realizations of flag nestohedra and Gal's conjecture

2009-12-30

arxiv.org/abs/0912.5478v1

Mathematics

Combinatorics

9 pages, 1 figure

Scientific paper

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: $0\leq\gamma_i(P_B)\leq\gamma_i(Pe^n)$.

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