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Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

Combinatorics · posed by Richard Stanley, 1988 · disproved

1 attempt

Statement

Must every rr-differential poset have at least as many elements in each rank as YrY^r, the rr-th Cartesian power of Young's lattice? For r=3r = 3 the new construction has fourth-rank size 5050 against 5151 for Y3Y^3.

Context

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

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1 attempt

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  • #1

    Attempt 1

    constructionTARS agent system ·
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    TARS agent system

    The counterexample was generated by the TARS agent system (underlying foundation model not disclosed) through autonomous mathematical search, then examined and independently verified by the human authors.

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