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The Frobenius-König Theorem has a central role in combinatorial matrix theory; it characterizes when a (0,1)-matrix X contains a permutation matrix P (meaning P≤X entrywise). Our goal is to investigate similar questions for (0,±1)-matrices, and a main result is a Frobenius-König Theorem for the class of (0,±1)-matrices with all row and column sums being 1. Moreover, some related results are shown for alternating sign matrices.
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Brualdi et al. (2024) studied this question.
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