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Mixed Partition Functions and Exponentially Bounded Edge-Connection Rank

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regts-sevenster-mixed-partition-functionsCombinatoricsposed by Guus Regts and Bart Sevensterrecorded: solved

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Statement

Regts and Sevenster conjectured that a complex-valued graph parameter ff with f(∅)=1f(\varnothing)=1 has exponentially bounded edge-connection rank precisely when it is a mixed partition function. The paper proves it, with the numbers of even and odd colours bounded in terms of the rank bound.

Context

A named conjecture of Regts and Sevenster characterising which graph parameters are partition functions, a central question in the area.

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  • #1

    Attempt 1

    proof attemptClaude Fable 5 + GPT-5.6 Sol Pro with William Whistler ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    Claude Fable 5 + GPT-5.6 Sol Pro
    people
    William Whistler

    The acknowledgements say only that Claude Fable 5 and GPT-5.6 Sol Pro "were used extensively in the development and preparation of this work". That does not separate mathematical contribution from writing, so the lowest tier applies; read the disclosure rather than the tier.

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