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Stanley's Problem 4 on Differential Posets

Combinatorics · posed by Richard Stanley, 1988 · disproved

1 attempt

Statement

For a differential poset PP, must the weighted 22-multichain series MP,2(q)M_{P,2}(q) be a rational multiple of FP(q)2F_P(q)^2, the square of its rank generating series?

Context

From Stanley's 1988 differential-posets paper, a recognized source of problems.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionTARS agent system ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    TARS agent system

    The construction was found by the TARS agent system (foundation model not disclosed); the proof was reconstructed and manually verified by the human authors.

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