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Real-Rootedness of Ehrhart h*-Polynomials at Large Width

Combinatorics · posed by Gennadiy Averkov, Johannes Hofscheier, Benjamin Nill · solved

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Statement

A question of Averkov, Hofscheier and Nill on whether the Ehrhart h∗h^*-polynomial of a lattice polytope of large lattice width is real-rooted. Proved in fixed dimension for sufficiently large lattice width, giving strict log-concavity and unimodality of the h∗h^*-vector, with the analogous statement for the local h∗h^*-polynomial of a lattice simplex.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    ChatGPT 5.6 Sol, with Benjamin Nill

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

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    — the result was found by a model.

    The acknowledgments state that the proofs were found using ChatGPT 5.6 Sol, which also produced a first draft of the paper, with the author solely responsible for the final version.

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