Geodesic
A~combinatorial approach to the enumeration of doubly stochastic square matrices with nonnegative integer elements
Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 90-101.

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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. 
@article{DM_1993_5_3_a7,
     author = {E. E. Marenich},
     title = {A~combinatorial approach to the enumeration of doubly stochastic square matrices with nonnegative integer elements},
     journal = {Diskretnaya Matematika},
     pages = {90--101},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1993_5_3_a7/}
}
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E. E. Marenich. A~combinatorial approach to the enumeration of doubly stochastic square matrices with nonnegative integer elements. Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 90-101. http://geodesic.mathdoc.fr/item/DM_1993_5_3_a7/