Séminaire Lotharingien de Combinatoire, 89B.67 (2023), 12 pp.
Ezgi Kantarcı Oğuz, Cem Yalım Özel and Mohan Ravichandran
Chainlink Polytopes
Abstract.
We introduce a class of polytopes that we call chainlink polytopes and which allow us to construct infinite families of pairs of non isomorphic rational polytopes with the same Ehrhart quasi-polynomial. Our construction is inspired by a non-obvious and non-trivial symmetry in the rank sequences of circular fence posets. We show that this symmetry can be lifted to yield an analogous symmetry at the level of polytopes. We show this symmetry property of Chainlink polytopes by introducing the related class of chainlink posets and show that they exhibit the same symmetry properties using linear algebraic techniques. We further prove an outstanding conjecture on the unimodality of circular rank polynomials.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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