The $h^*$-Polynomial of the Order Polytope of the Zig-Zag Poset
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Published:2023-06-16
Issue:2
Volume:30
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Coons Jane Ivy,Sullivant Seth
Abstract
We construct a family of shellings for the canonical triangulation of the order polytope of the zig-zag poset. This gives a new combinatorial interpretation for the coefficients in the numerator of the Ehrhart series of this order polytope in terms of the swap statistic on alternating permutations. We also offer an alternate proof of this result using the techniques of rank selection. Finally, we show that the sequence of coefficients of the numerator of this Ehrhart series is symmetric and unimodal.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics