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Simon's Extendable Shellability Conjecture

Combinatorics · posed by Robert Simon, 1994 · disproved

2 comments

Statement

Simon conjectured that every skeleton of a simplex is extendably shellable. False: for every d≥3d \ge 3 there is a pure dd-dimensional shellable simplicial complex that is not shelling completable.

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

  1. construction · #1

    Davide Bolognini and Paolo Sentinelli, using ChatGPT 5.5

    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 co developed
    — a person and a model developed the result together.

    The paper says the contractible simplicial complex behind the counterexample was identified with the assistance of ChatGPT 5.5, and that the published version reaches the same complex through exhaustive computation.

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed site check

    scope Reproduction by the VibeMathed site

    The refutation is an explicit finite simplicial complex, reproduced by exhaustive computation in the paper, so it is a finite check. arXiv preprint, not peer-reviewed.

    Repeated from the source; nothing was checked here.

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