algebra / Linear Algebra, Permanents
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 $n\ge16$.
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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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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 $n\ge16$.
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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