Krishna Menon: Combinatorial gamma-positivity for octopuses

Abstract: Athanasiadis, Xiao, and Yan recently studied a nice class of polytopes called octopus polytopes. These are a special class of arbor polytopes, introduced by Chapoton. One of the polynomials they study counts lattice points in the polytope by number of nonzero coordinates. They prove that this polynomial is gamma-positive for octopus polytopes. Since their proof was computational, they asked for one that is bijective. We present such a proof.