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Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

Combinatorics · posed by Richard Stanley, 1988 · disproved

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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.

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

  1. construction · #1

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