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Rota's Unimodality Conjecture for Matroid Flats

Combinatorics · posed by Gian-Carlo Rota, 1970 · disproved

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Statement

Is the sequence W0,W1,…,WnW_0, W_1, \dots, W_n counting the flats of each rank of a matroid always unimodal? Rota conjectured yes in 1970.

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

  1. construction · #1

    Alexander Divoux, Chayim Lowen and Shouda Wang, using ChatGPT-5.6 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    A counterexample to the convexity of the sequence Wi−1W_i^{-1} was found with ChatGPT-5.6 Pro following a suggestion of the authors. This matroid was constructed using Whittle's qq-lift mechanism, which the authors then adapted into a counterexample for unimodality.

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