Dittert's Conjecture in Dimension 16

Dittert's conjecture asserts that among nonnegative $n\times n$ matrices whose entries sum to $n$ , the functional $\varphi(A)=\prod_i r_i+\prod_j c_j-\operatorname{per}(A)$ is uniquely maximized by $J_n/n$ . The paper proves the case $n=16$ which, with Pang's result for $n\ge17$ , establishes the conjecture for every $n\ge16$ .

Result: Proved(see note)
Status: Partial result
AI contribution: AI-discovered
Method: Argument
Field: Linear Algebra, Permanents
Posed by: Eberhard Dittert
Year posed: —
Years open: —
Solved: 2026-07-21
Model: GPT-5.6 Sol
Vendor: OpenAI
Collaborators: Boris Kafidov
Verification: Unreviewed
Publication: Preprint
Significance: 15 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What was actually shown

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

What the AI did

The disclosure states 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.

Verification

No independent check, and the model is credited with the strategy and the central lemma rather than with support. Preprint, not refereed.

Source

PaperarXiv

Related entries

RelatedDittert n=5