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Elizalde-Luo Pattern-Avoidance Conjecture

Combinatorics · posed by Sergi Elizalde & Luo, 2025 · solved

1 attempt · 1 machine check

Statement

Is the number of nonnesting permutations of {1,1,…,n,n}\{1,1,\dots,n,n\} avoiding both 11321132 and 33123312 equal to 3n−3⋅2n−1+13^n - 3 \cdot 2^{n-1} + 1 for every n≥1n \ge 1?

Context

A recent conjecture from a single combinatorics paper.

People

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Attempts

1 attempt

No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

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  • #1

    Attempt 1

    proof attemptDemonstrandum multi-agent pipeline ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Demonstrandum multi-agent pipeline

    Found by the Demonstrandum multi-agent pipeline; every refutation ships a finite certificate, a mutation-tested checker, and an independent clean-room recomputation.

    Reviews

    1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      scope Lean formalization of the result

      Proved and Lean-checked end to end; not externally refereed.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

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