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A combinatorial approach to the enumeration of doubly stochastic square matrices with nonnegative integer elements
E. E. Marenich
Abstract:
Let $H_R(n,r)$ be equal to the number of $n\times n$ matrices with non-negative integer elements such that all row sums and all column sums are equal to $r$ and all elements with indices from a set $R$ are equal to zero. We investigate the properties of the function $H_R(n,r)$ and give a combinatorial interpretation of the obtained results.
Received: 21.10.1991
Citation:
E. E. Marenich, “A combinatorial approach to the enumeration of doubly stochastic square matrices with nonnegative integer elements”, Diskr. Mat., 5:3 (1993), 90–101; Discrete Math. Appl., 3:6 (1993), 649–661
Linking options:
https://www.mathnet.ru/eng/dm694 https://www.mathnet.ru/eng/dm/v5/i3/p90
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