ProbXiv
sign in
Problem archiveProblem record

The Order of Long Rainbow Arithmetic Progressions

Combinatorics · posed by Veselin Jungic, Jacob Licht, Mohammad Mahdian, Jaroslav Nesetril, Rados Radoicic, 2003 · disproved

1 comment

Statement

Let TkT_k be the least tt such that every equinumerous tt-coloring of [tn][tn] contains a rainbow kk-term arithmetic progression. Jungic, Licht, Mahdian, Nesetril and Radoicic conjectured Tk=Θ(k2)T_k = \Theta(k^2); Conlon, Fox and Sudakov proved Tk=O(k2log⁡k)T_k = O(k^2 \log k). The matching lower bound Tk=Ω(k2log⁡k)T_k = \Omega(k^2 \log k) holds, so Tk=Θ(k2log⁡k)T_k = \Theta(k^2 \log k) and the conjectured order is wrong.

Record

Source
Added

Comments

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

  1. construction · #1

    Jesse Geneson, using Codex (GPT-5.6), Claude Code (Fable 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 assisted
    — a person led the work and used a model along the way.

    The acknowledgement says the two systems were used for proof exploration, proof criticism, exposition and revision. Proof exploration and criticism are mathematical work rather than prose work, but no specific step is attributed, so the lowest tier applies.

    the true order is determined, and it is not the conjectured one

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.