Work

Real-rooted Ehrhart $h^*$-polynomials of crown posets and wheel and whirl matroids

Year: 2026

Type: preprint

Abstract: We prove that the Ehrhart $h^*$-polynomials of crown order polytopes are real-rooted, settling a conjecture of Lundström and Saud Maia Leite. For each integer $r\ge3$, the crown order polytope on $2r$ elements and the rank-$r$ whirl base polytope have the same $h^*$-polynomial. The $h^*$-polynomials of the rank-$r$ wheel and whirl base polytopes, as well as every convex combination of the two, have $2r-2$ distinct negative roots. Their coefficient sequences are positive, unimodal, and strictly ultra log-concave of order $2r-2$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.40496

Authors: Cao, Ying, Fu, Houshan

Institutions: Hong Kong University of Science and Technology, Guangzhou University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Basic and Applied Basic Research Foundation of Guangdong Province

OpenAlex ID: W7224965809

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