An identity involving h-polynomials of poset associahedra and type B Narayana polynomials

2024/07/05 by Son Nguyen, Nguyen, Son
Agricultural and Biological Sciences · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Leaf Properties and Growth Measurement

paper · pdf · doi:10.48550/arxiv.2407.04517

openalex publication_date 2024/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any finite connected poset P, Galashin introduced a simple convex (|P|-2)-dimensional polytope \mathscrA(P) called the poset associahedron. Let P be a poset with a proper autonomous subposet S that is a chain of size n. For 1≤ i ≤ n, let P_i be the poset obtained from P by replacing S by an antichain of size i. We show that the h-polynomial of \mathscrA(P) can be written in terms of the h-polynomials of \mathscrA(P_i) and type B Narayana polynomials. We then use the identity to deduce several identities involving Narayana polynomials, Eulerian polynomials, and stack-sorting preimages.

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