宽幅格多面体具有实根Ehrhart h*-多项式
Lattice polytopes of large width have real-rooted Ehrhart $h^*$-polynomials
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中文总结 AI 辅助
该研究证明固定维数下宽幅格多面体的Ehrhart h*-多项式为实根，还给出格单纯形局部h*-多项式的类似结论，解答了相关问题，证明借助ChatGPT 5.6 Sol完成。
中文摘要 AI 辅助
在本文中，我们证明：固定维数下，足够大格宽的格多面体的Ehrhart h*-多项式是实根的。这特别意味着h*-向量具有严格对数凹性和单峰性，回答了Averkov、Hofscheier及本文作者提出的问题。对于格单纯形，我们证明其局部h*-多项式（亦称盒多项式）也有类似结论。证明借助ChatGPT 5.6 Sol完成，本质上直接源自Basu与Oertel的结果：当格宽足够大时，格点计数近似体积。
英文摘要
In this note we prove that in fixed dimension the Ehrhart $h^*$-polynomial of a lattice polytope of sufficiently large lattice width is real-rooted. In particular, this implies strict log-concavity and unimodality of the $h^*$-vector and answers a question of Averkov, Hofscheier and the author. For a lattice simplex we prove the analogous statement for its local $h^*$-polynomial, also called box polynomial. The proofs were found using ChatGPT 5.6 Sol and follow essentially directly from a result by Basu and Oertel that for large enough lattice width counting lattice points approximates the volume.
