ProbXiv
sign in
Problem archiveProblem record

Reiner's Conjecture on Higher Bruhat Orders in Corank 3

Combinatorics · posed by Victor Reiner · partial

1 comment

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.

Record

Source
Added

Comments

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

  1. proof attempt · #1

    Daria Poliakova, using ChatGPT Pro (5.5, 5.6 Sol)

    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 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

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.