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Mixed Partition Functions and Exponentially Bounded Edge-Connection Rank

Combinatorics · posed by Guus Regts and Bart Sevenster · 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.

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

  1. proof attempt · #1

    William Whistler, using Claude Fable 5 + GPT-5.6 Sol 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 assisted
    — a person led the work and used a model along the way.

    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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