algebra / Matrix theory
For the set of $n \times n$ doubly stochastic matrices, Kim and Roush conjectured in 1981 that for odd $n = 2k+1 > 1$ the maximum of $\mathrm{per}(I-A)$ equals $3 \cdot 2^{k-2}$, attained by an explicit block construction. Proved in full, and the maximizers are classified: they are exactly the simultaneous-permutation conjugates of that construction.
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Append-only history
Kim and Roush did not claim uniqueness; the classification of equality cases is new alongside the conjecture itself.
Research memory
For the set of $n \times n$ doubly stochastic matrices, Kim and Roush conjectured in 1981 that for odd $n = 2k+1 > 1$ the maximum of $\mathrm{per}(I-A)$ equals $3 \cdot 2^{k-2}$, attained by an explicit block construction. Proved in full, and the maximizers are classified: they are exactly the simultaneous-permutation conjugates of that construction.
Kim and Roush did not claim uniqueness; the classification of equality cases is new alongside the conjecture itself.
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