ProbXiv
sign in
Problem archiveProblem record

The Abbott-Hanson Recurrence for Schur Numbers

Combinatorics · posed by Harvey Abbott, Denis Hanson, 1972 · partial

1 comment

Statement

The classical Abbott-Hanson recurrence gives S(k+2)≥9S(k)+4S(k+2) \ge 9S(k)+4 for Schur numbers, and had stood as the basis for the best asymptotic lower bounds. Shifted SS-templates, a more flexible form of Rowley's template construction, yield S(k+2)≥10S(k)+2S(k+2) \ge 10S(k)+2 and hence improved lower bounds.

Record

Source
Added

Comments

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

  1. construction · #1

    Nils Bengone, Amine Brouk, Max Grinsztajn, Terence Helbert, Bao Lugherini, Arpad Rimmel and Joanna Tomasik, using ChatGPT 5.5 Pro

    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 abstract says the shifted SS-template construction was discovered during a conversation with ChatGPT 5.5 Pro and then refined, verified and extended to multiple templates by the authors, and the conclusion describes the paper as building on an original idea of the model.

    improves the classical recurrence; the exact Schur numbers beyond S(5) remain unknown

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.