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Diskretnaya Matematika, 1993, Volume 5, Issue 3, Pages 90–101 (Mi dm694)  

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
Bibliographic databases:
UDC: 519.1
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Mar93}
\by E.~E.~Marenich
\paper A~combinatorial approach to the enumeration of doubly stochastic square matrices with nonnegative integer elements
\jour Diskr. Mat.
\yr 1993
\vol 5
\issue 3
\pages 90--101
\mathnet{http://mi.mathnet.ru/dm694}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1266261}
\zmath{https://zbmath.org/?q=an:0799.05003}
\transl
\jour Discrete Math. Appl.
\yr 1993
\vol 3
\issue 6
\pages 649--661
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