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New Bounds for Double Covers of the Discrete Box

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double-covers-discrete-boxCombinatoricsposed by Leader, Miličević and Tanrecorded: partial

1 attempt · no person has looked

Statement

For A={0,1,2}dA=\{0,1,2\}^d, write f(d)f(d) for the fewest proper sub-boxes covering every point exactly twice. Leader, Miličević and Tan asked whether f(d)≥2df(d)\ge 2^d for all dd, as Question 4.1 of the PatternBoost paper. The paper gives new bounds on f(d)f(d).

Context

Improved bounds rather than a settled question: the asked-for inequality is not established in general.

Progress on a question posed in the PatternBoost paper, itself a study of machine-assisted mathematics.

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1 attempt

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  • #1

    Attempt 1

    constructionClaude with Patrick White ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    Claude
    people
    Patrick White

    The author credits large language models used as reasoning engines with producing several of the key ideas, naming the modular refinement of Section 3, the crossing lemma of Section 5 and the constructions of Section 7.

    Improved bounds rather than a settled question: the asked-for inequality is not established in general.

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