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- W2068234920 abstract "We consider the set of n × n matrices X =( x ij ) for which ∑ iϵI ∑ jϵJ x ij ⩾ | I |+| J |− n , for all I , J ⊆ {1, 2,…, n }, with x ij ⩾ 0 for all i , jϵ {1, 2,…, n }. It is shown that such matrices may be decomposed as X = S + N , where S is a doubly stochastic matrix and N is non-negative in all entries. The decomposition technique is constructive. This implies a result of Fulkerson that the matrices X , considered as lying in R n 2 form a convex polyhedron whose vertices are the permutation matrices. Finally, a subset of the inequalities of (1) is shown to be “essential”, as asserted by Fulkerson in [1] without proof." @default.
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- W2068234920 date "1971-09-01" @default.
- W2068234920 modified "2023-10-18" @default.
- W2068234920 title "A constructive decomposition and Fulkerson's characterization of permutation matrices" @default.
- W2068234920 doi "https://doi.org/10.1016/0012-365x(71)90026-4" @default.
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