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Nine Ramsey Number Lower-Bound Records

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ramsey-lower-bound-records-alphaevolveCombinatoricsposer not recordedrecorded: partial

1 attempt · no person has looked

Statement

Improved lower bounds for nine classical Ramsey numbers, including R(3,13)≥61R(3,13) \geq 61, R(3,18)≥100R(3,18) \geq 100, and seven R(4,k)R(4,k) records up to R(4,20)≥237R(4,20) \geq 237, found by AlphaEvolve-discovered search algorithms.

Context

Records, not resolutions: the exact values of these Ramsey numbers remain unknown.

Small Ramsey numbers are among combinatorics' most famous open quantities, tracked for decades in Radziszowski's dynamic survey.

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  • #1

    Attempt 1

    constructionAlphaEvolve with Ansh Nagda, Prabhakar Raghavan, Abhradeep Thakurta ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    AlphaEvolve
    people
    Ansh Nagda, Prabhakar Raghavan, Abhradeep Thakurta

    AlphaEvolve, an LLM-based code-mutation system, ran a meta-search that discovered the search algorithms which produced the record constructions; Gemini 3 summarized the generated code for the paper.

    Records, not resolutions: the exact values of these Ramsey numbers remain unknown.

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