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arXiv · 2409.16648

A new class of magic positive Ehrhart polynomials of reflexive polytopes

Masato Konoike
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Abstract

The magic positivity of Ehrhart polynomials is a useful tool for proving the real-rootedness of the $h^\ast$-polynomials. In this paper, we provide a new class of reflexive polytopes whose Ehrhart polynomials are magic positive. First, we prove that the Ehrhart polynomials of Stasheff polytopes are magic positive. Second, we provide a partial proof of the magic positivity of the Ehrhart polynomials of the dual polytopes of the symmetric edge polytopes of cycles.

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BibTeXRIS

Masato Konoike. 2025-07-02. A new class of magic positive Ehrhart polynomials of reflexive polytopes. https://arxiv.org/abs/2409.16648

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