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Restricted Chain-Order Polytopes via Combinatorial Mutations

Oliver Clarke, Akihiro Higashitani, Francesca Zaffalon

Submitted on 15 November 2022

Abstract

We study restricted chain-order polytopes associated to Young diagrams using combinatorial mutations. These polytopes are obtained by intersecting chain-order polytopes with certain hyperplanes. The family of chain-order polytopes associated to a poset interpolate between the order and chain polytopes of the poset. Each such polytope retains properties of the order and chain polytope; for example its Ehrhart polynomial. For a fixed Young diagram, we show that all restricted chain-order polytopes are related by a sequence of combinatorial mutations. Since the property of giving rise to the period collapse phenomenon is invariant under combinatorial mutations, we provide a large class of rational polytopes that give rise to period collapse.

Preprint

Comment: 18 pages, 3 figures

Subjects: Mathematics - Combinatorics; 52B20 (Primary) 52B05, 06A11, 14J33 (Secondary)

URL: http://arxiv.org/abs/2211.07995