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arXiv · 2609.00781

Palindromic real-rooted polynomials and $h$-vectors of polytopes

Peter L. Guo·Mingyang Kang
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Abstract

We prove that every monic palindromic real-rooted polynomial with nonnegative integer coefficients is the $h$-polynomial of a simplicial convex polytope. This resolves in the affirmative a longstanding problem circulated by Brenti since 2004.

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Peter L. Guo, Mingyang Kang. 2026-09-01. Palindromic real-rooted polynomials and $h$-vectors of polytopes. https://arxiv.org/abs/2609.00781

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