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Stanley's Claw-Free Schur-Positivity Conjecture

Combinatorics · posed by Richard Stanley, 1995 · disproved

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Statement

Is the chromatic symmetric function XGX_G Schur positive for every claw-free graph GG? Two explicit 1212-vertex line graphs have Schur coefficients −64-64 and −40-40 at s(3,3,3,3)s_{(3,3,3,3)}.

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

  1. construction · #1

    ChatGPT-5.6 Sol Pro

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

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

    Both counterexample graphs were found with ChatGPT-5.6 Sol Pro; the negative coefficients were confirmed by independent computations.

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