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Ehrhart Positivity of Schubitopes

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schubitope-ehrhart-positivityCombinatoricsposed by Cara Monical, Neriman Tokcan, Alexander Yong, 2019recorded: disproved

1 attempt · no person has looked

Statement

Monical, Tokcan and Yong conjectured that Schubitopes, the generalized permutahedra arising as Newton polytopes of Schubert polynomials and of Demazure characters of GLn\mathrm{GL}_n, are Ehrhart positive. Disproved by an explicit Schubitope whose Ehrhart polynomial has a negative coefficient in its monomial expansion.

Context

Conjecture 5.19 of Monical, Tokcan and Yong's Newton polytopes paper, in the line of Ferroni's disproof of Ehrhart positivity for matroid polytopes.

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  • #1

    Attempt 1

    constructionGPT-5.6 Sol Pro with Yupeng Li, Avery St. Dizier ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6 Sol Pro
    people
    Yupeng Li, Avery St. Dizier

    The abstract states the counterexample was found using GPT-5.6 Sol Pro in ChatGPT. The authors supply the surrounding treatment of the family.

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