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Let A(R,S) denote the class of all matrices of zeros and ones with row sum vector R and column sum vector S. We introduce the notion of an inversion in a (0,1)-matrix. This definition extends the standard notion of an inversion of a permutation, in the sense that both notions agree on the class of permutation matrices. We prove that the number of inversions in a (0,1)-matrix is monotonic with respect...
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