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Conjecture on $k$-Antichains in the Unit Cube

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k-antichains-unit-cubeCombinatoricsposed by conjecture in the antichain-measure literaturerecorded: solved

1 attempt · no person has looked

Statement

A subset AA of the pointwise-ordered cube [0,1]n[0,1]^n is a kk-antichain when it meets every chain in at most kk points. The conjecture concerns the largest possible (n−1)(n-1)-dimensional Hausdorff measure of such a set; it is settled here, following work of Janzer.

Context

A specific conjecture on Hausdorff measure of antichains in the cube, with a small but real following after Janzer's work on it.

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1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.5 Pro with John M. Campbell ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5.5 Pro
    people
    John M. Campbell

    The paper states that the construction carrying the proof is largely based on the author's extensive interactions with GPT-5.5 Pro.

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