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The Kim-Roush Conjecture on the Maximum of per(I-A) in Odd Order

Algebra · posed by Ki Hang Kim, Fred W. Roush, 1981 · solved

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Statement

For the set of n by n doubly stochastic matrices, Kim and Roush conjectured in 1981 that for odd n = 2k+1 > 1 the maximum of per(I-A) equals 3 times 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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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.6 Sol and Claude Fable 5, with Yair Lavi

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    The acknowledgments are one sentence and leave nothing to interpret: "The proof of this conjecture was carried out by GPT-5.6-sol and Claude Fable 5, under the guidance of the author. The author has reviewed the resulting proof arguments. Responsibility for the final text rests with the author."

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