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Fulek's Question on the Extremal Function of L_3

Combinatorics · posed by Radoslav Fulek, 2009 · solved

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Statement

Fulek defined a weight-five three-row 00-11 matrix L3L_3 and asked whether ex(n,L3)=O(n)\mathrm{ex}(n, L_3) = O(n). It is: every r×sr \times s matrix avoiding L3L_3 has at most 27r+2s27r + 2s ones, so 6n−8≤ex(n,L3)≤29n6n - 8 \le \mathrm{ex}(n,L_3) \le 29n for n≥5n \ge 5. The same argument covers an infinite family of light three-row patterns, verifying a conjecture of Pettie and Tardos on linear light patterns for that family.

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

  1. proof attempt · #1

    Jesse Geneson, using Codex (GPT-5.6), Claude Code (Fable 5)

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The acknowledgement says the two systems were used for proof exploration, proof criticism, exposition and revision, with no specific step attributed, so the lowest tier applies.

    the companion pattern Fulek proposed alongside L_3 is not covered by this method

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