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A Bruhat order for the class of (0,1)-matrices with row sum vector R and column sum vector S

2005
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The Electronic Journal of Linear Algebra
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Generalizing the Bruhat order for permutations (so for permutation matrices), a Bruhat order is defined for the class of m by n (0, 1)-matrices with a given row and column sum vector. An algorithm is given for constructing a minimal matrix (with respect to the Bruhat order) in such a class. This algorithm simplifies in the case that the row and column sums are all equal to a constant k. When k = 2 or k = 3, all minimal matrices are determined. Examples are presented that suggest such a

doi:10.13001/1081-3810.1141
fatcat:td6brxyin5f63psgcaseazpnya