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Reiner's Conjecture on Higher Bruhat Orders in Corank 3

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reiner-conjecture-corank-threeCombinatoricsposed by Victor Reinerrecorded: partial

1 attempt · no person has looked

Statement

Reiner conjectured a description of the homotopy types of intervals in higher Bruhat orders. In corank 33 it holds: the facial intervals of B(n,n−3)B(n,n-3) are exactly the spherical intervals, and every other interval is contractible.

Context

corank 3; the general conjecture remains open, corank 2 being McConville's case

A named conjecture on higher Bruhat orders in the Manin-Schechtman and Ziegler tradition, with a small specialist readership in poset topology.

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1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT Pro (5.5, 5.6 Sol) with Daria Poliakova ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT Pro (5.5, 5.6 Sol)
    people
    Daria Poliakova

    The AI use declaration lists the model as search engine, proof assistant, vector graphics artist and editor, and states that all outputs of the proof assistant were thoroughly digested by a human and that the exposition is by and for humans.

    corank 3; the general conjecture remains open, corank 2 being McConville's case

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