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Palindromic real-rooted polynomials and h-vectors of polytopes
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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BibTeX
@misc{guo2026palindromic,
title = {{Palindromic real-rooted polynomials and $h$-vectors of polytopes}},
author = {Peter L. Guo and Mingyang Kang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00781},
eprint = {2609.00781},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00781},
}
RIS
TY - UNPB
TI - Palindromic real-rooted polynomials and h-vectors of polytopes
AU - Peter L. Guo
AU - Mingyang Kang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00781
UR - https://arxiv.org/abs/2609.00781
AB - 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.
ER -