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

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averkov-hofscheier-nill-h-star-real-rootednessCombinatoricsposed by Gennadiy Averkov, Johannes Hofscheier, Benjamin Nillrecorded: 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.

Context

A stated question in Ehrhart theory, where unimodality of the h*-vector has been a recurring target; the answer follows from a result of Basu and Oertel once the right reduction is seen.

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  • #1

    Attempt 1

    proof attemptChatGPT 5.6 Sol with Benjamin Nill ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    ChatGPT 5.6 Sol
    people
    Benjamin Nill

    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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