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- W2084941670 abstract "This paper considers the existence of triangular matrices with specified row and column sums. Let R =( r 1 , r 2 ,…, r m ) and S =( s 1 , s 2 ,…, s n ) be vectors with nonnegative integral entries. Then U (R,S) is the set of m x n (0,1)-matrices with i th row sum r i and j th column sum s j . Let m = n and let U (R,S) be nonempty with r 1 ⩾ r 2 ⩾⋯⩾ r n , s 1 ⩾ s 2 ⩾⋯⩾ s n . Then these exists a matrix in U (R,S) with a triangular block of 0′s if and only if r i ⩽ n - i +1 and s i ⩽ n - i +1 for 1⩽ i ⩽ n . These are the simplest conditions one could hope for and are a substantial simplificationof network flow conditions that can be obtained. Using our result one can obtain that there is a matrix A ϵ U ( R , S ) with per( A )=1 if and only if there is a matrix Aϵ U (R,S) with A ⩾ P for some permutation matrix P (easy to check) and the above inequalities hold." @default.
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- W2084941670 date "1982-01-01" @default.
- W2084941670 modified "2023-09-26" @default.
- W2084941670 title "Triangular (0,1)-matrices with prescribed row and column sums" @default.
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- W2084941670 doi "https://doi.org/10.1016/0012-365x(82)90182-0" @default.
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