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Stanley's Claw-Free Schur-Positivity Conjecture

Combinatorics · posed by Richard Stanley, 1995 · disproved

1 attempt

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)}.

Context

Stanley's claw-free positivity question, a standing target in symmetric function theory.

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1 attempt

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  • #1

    Attempt 1

    constructionChatGPT-5.6 Sol Pro ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    ChatGPT-5.6 Sol Pro

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

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