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White's Conjecture on Matroids

Combinatorics · posed by Neil White, 1980 · disproved

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Statement

White conjectured that the symmetric exchange binomials generate the toric ideal of a matroid. This is now known to be false; a rank 99 binary matroid constitutes a counterexample.

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

  1. construction · #1

    ChatGPT-5.5 Pro, Claude Opus 4.8, with Matt Larson

    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.

    AI involvement
    ai discovered
    — the result was found by a model.

    The author prompted ChatGPT-5.5 Pro to check White's conjecture and it claimed to prove the result for ranks 55 and 66. After further prompting to check for random matroids of ranks 77, 88, 99, and 1010, it found a matroid isomorphic to the given counterexample.

    ChatGPT-5.5 Pro and Claude Opus 4.8 were used for proofreading and generating the figures.

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