Geodesic
Random partitions of sets with marked subsets
Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 485-498 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We are given a uniform probability distribution on the partitions of a set $X$ of $m$ elements. For each realization of the random partition we define a random process of drawing marks: every subset of cardinality $k$ receives a mark with probability $p_k$. We find expressions for exact distributions of the number of marked subsets of cardinality $l$, the overall number of marked subsets and the number of elements in them. For certain concrete values $p_k=p_k(m)$, $k=1,2,\dots,$ we obtain the limit distributions of these random variables as $m\to\infty$. Bibliography: 8 titles. 
@article{SM_1973_21_3_a9,
     author = {V. N. Sachkov},
     title = {Random partitions of sets with marked subsets},
     journal = {Sbornik. Mathematics},
     pages = {485--498},
     year = {1973},
     volume = {21},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_3_a9/}
}
TY  - JOUR
AU  - V. N. Sachkov
TI  - Random partitions of sets with marked subsets
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 485
EP  - 498
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1973_21_3_a9/
LA  - en
ID  - SM_1973_21_3_a9
ER  - 
%0 Journal Article
%A V. N. Sachkov
%T Random partitions of sets with marked subsets
%J Sbornik. Mathematics
%D 1973
%P 485-498
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1973_21_3_a9/
%G en
%F SM_1973_21_3_a9
V. N. Sachkov. Random partitions of sets with marked subsets. Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 485-498. http://geodesic.mathdoc.fr/item/SM_1973_21_3_a9/

[1] Dzh. Riordan, Vvedenie v kombinatornyi analiz, IL, Moskva, 1963

[2] N. G. de Brein, Asimptoticheskie metody v analize, IL, Moskva, 1961

[3] L. Moser, M. Wyman, “An asymptotic formula for the Bell numbers”, Trans. Roy. Soc. Canada, 49 (1955), 49–54 | MR | Zbl

[4] L. H. Harper, “Stiriling behavior is asymptotically normal”, Ann. Math. Statist., 38:2 (1967), 410–414 | DOI | MR | Zbl

[5] A. Renyi, “Uj modzerek és eredmemy a kombinatorikus analizisben, I”, Magyar. Tud. Akad. Mat. Fiz., Tud. Oszt. Közl., 16:1 (1966), 77–105 | MR | Zbl

[6] I. H. Curtiss, “A note on the theory of moment generating functions”, Ann. Math. Statist., 13:3 (1942), 430–433 | DOI | MR | Zbl

[7] V. N. Sachkov, Perechislitelnye metody kombinatornogo analiza, Voprosy kombinatornoi matematiki. Izd. nauchnogo soveta po kompleksnoi probleme kibernetika, AN SSSR, Moskva, 1973 | Zbl

[8] V. N. Sachkov, “Raspredelenie chisla razlichnykh elementov simmetrichnogo bazisa v sluchainoi $mA$-vyborke”, Teoriya veroyatnostei, XVI:3 (1971), 504–513