Geodesic
Comparisons modulo a~prime for the number of $(0,1)$-matrices
Diskretnaya Matematika, Tome 2 (1990) no. 3, pp. 153-157

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Let $B$ be a set of $(0,1)$ $n\times n$ matrices such that if $M\in B$ and $M'$ is obtained from $M$ by an arbitrary rearrangement of rows and columns, then $M'\in B$. For prime $p$ we find comparisons modulo $p$ for $|B|$, where $|B|$ is the number of elements in $B$. We consider applications of this result in cases when $B$ is 1) a set of matrices with a permanent equal to $r$, $r\in\mathbb N_0=\{0,1,2,\cdots\}$; 2) a set of matrices with given row and column sums. 
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     author = {E. E. Marenich},
     title = {Comparisons modulo a~prime for the number of $(0,1)$-matrices},
     journal = {Diskretnaya Matematika},
     pages = {153--157},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1990_2_3_a17/}
}
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E. E. Marenich. Comparisons modulo a~prime for the number of $(0,1)$-matrices. Diskretnaya Matematika, Tome 2 (1990) no. 3, pp. 153-157. http://geodesic.mathdoc.fr/item/DM_1990_2_3_a17/