Inequalities between Gamma-Polynomials of Graph-Associahedra

Natalie Aisbett

Abstract


We prove a conjecture of Postnikov, Reiner and Williams by defining a partial order on the set of tree graphs with $n$ vertices that induces inequalities between the $\gamma$-polynomials of their associated graph-associahedra. The partial order is given by relating trees that can be obtained from one another by operations called tree shifts. We also show that tree shifts lower the $\gamma$-polynomials of graphs that are not trees, as do the flossing moves of Babson and Reiner.

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