Dittert's Conjecture in Dimension Five
Prior state unknown→proved
Dimension 5 only; public AI-generated candidate with no independent specialist review.
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combinatorics / Linear algebra; permanents; exact sum-of-squares certificates
Dittert's Conjecture in Dimension Five
The dimension-five case asks whether, for every nonnegative $5\times5$ real matrix $A$ whose entries sum to $5$, the Dittert functional $\Phi(A)=\prod_i r_i+\prod_j c_j-\operatorname{per}(A)$ is uniquely maximized at $U_5=J_5/5$. The submitted artifact claims the stronger quantitative bound $$\Phi(A)\leq \frac{1226}{625}-\frac{1}{625}\lVert A-U_5\rVert_F^2,$$ which implies uniqueness.
15Significance / 100
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The dimension-five case asks whether, for every nonnegative $5\times5$ real matrix $A$ whose entries sum to $5$, the Dittert functional $\Phi(A)=\prod_i r_i+\prod_j c_j-\operatorname{per}(A)$ is uniquely maximized at $U_5=J_5/5$. The submitted artifact claims the stronger quantitative bound $$\Phi(A)\leq \frac{1226}{625}-\frac{1}{625}\lVert A-U_5\rVert_F^2,$$ which implies uniqueness.
Dimension 5 only; public AI-generated candidate with no independent specialist review.
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