Geodesic
Systems of distinct representatives for random sets
Sbornik. Mathematics, Tome 26 (1975) no. 3, pp. 365-371

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In this work estimates from below are obtained for the probability that the permanent of a random $n\times m$ $(0,1)$-matrix is positive. Using this estimate, it is shown that a random collection of subsets $X_1,\dots,X_n$ of the set $X$ of $m$ elements as $m\to\infty$ has a system of distinct representatives with probability close to one. Bibliography: 3 titles. 
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     author = {V. N. Sachkov},
     title = {Systems of distinct representatives for random sets},
     journal = {Sbornik. Mathematics},
     pages = {365--371},
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     number = {3},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_26_3_a4/}
}
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V. N. Sachkov. Systems of distinct representatives for random sets. Sbornik. Mathematics, Tome 26 (1975) no. 3, pp. 365-371. http://geodesic.mathdoc.fr/item/SM_1975_26_3_a4/