Geodesic
Systems of distinct representatives for random sets
Sbornik. Mathematics, Tome 26 (1975) no. 3, pp. 365-371 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
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     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/

[1] G. Dzh. Raizer, Kombinatornaya matematika, izd-vo «Mir», Moskva, 1966

[2] M. Kholl, Kombinatorika, izd-vo «Mir», Moskva, 1970 | MR

[3] C. I. Everett, P. R. Stein, “The asymptotic number of $(0,1)$-matrices with zero permanent”, Discrete Math., 6 (1973), 29–34 | DOI | MR | Zbl