Restricted Chain-Order Polytopes via Combinatorial Mutation

Chain-order polytopes form a family of polytopes interpolating between the classical order and chain polytopes of a poset. In this talk we will consider restricted chain-order polytopes, obtained via intersection with certain hyperplanes. While such restrictions are typically not lattice polytopes, they behave similarly to them. Indeed, many of these polytopes present Ehrhart period collapse: their Erhart functions are polynomial, as if they were lattice polytopes. For a fixed Young diagram we show that all restricted chain-order polytopes are related via combinatorial mutations, piecewise linear maps that preserve key geometric and enumerative structures of polytopes. This provides a large class of rational polytopes whose Ehrhart behavior mimics that of lattice polytopes.

Based on joint work with Oliver Clarke and Akihiro Higashitani.