The unimodality of the Ehrhart δ-polynomial of the chain polytope of the zig-zag poset

2016/03/28 by Herman Z. Q. Chen, Chen, Herman Z. Q., Philip B. Zhang +1 · 1 citation
Mathematics · #05A15 #05A20 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1603.08283

openalex publication_date 2016/03/28 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove the unimodality of the Ehrhart δ-polynomial of the chain polytope of the zig-zag poset, which was conjectured by Kirillov. First, based on a result due to Stanley, we show that this polynomial coincides with the W-polynomial for the zig-zag poset with some natural labeling. Then, its unimodality immediately follows from a result of Gasharov, which states that the W-polynomials of naturally labeled graded posets of rank 1 or 2 are unimodal.

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