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Dittert's Conjecture in Dimension 16

Algebra · posed by Eberhard Dittert · partial

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Statement

Dittert's conjecture asserts that among nonnegative n×nn\times n matrices whose entries sum to nn, the functional φ(A)=∏iri+∏jcj−per⁡(A)\varphi(A)=\prod_i r_i+\prod_j c_j-\operatorname{per}(A) is uniquely maximized by Jn/nJ_n/n. The paper proves the case n=16n=16 which, with Pang's result for n≥17n\ge17, establishes the conjecture for every n≥16n\ge16.

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

  1. proof attempt · #1

    GPT-5.6 Sol, with Boris Kafidov

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    The disclosure states that the proof strategy, the joint-deficit scaling lemma, and most of the original proof text were produced by GPT-5.6 Sol through ChatGPT in response to the author's prompts; ChatGPT also revised the exposition and prepared the manuscript.

    Partial: this settles n=16 only. Combined with Pang's n>=17 the conjecture holds for all n>=16, leaving the small cases open.

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