Geodesic
Random partitions of sets with a known number of blocks
Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 138-148.

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We consider the class of all partitions of a set of $n$ elements into $N$ blocks. Provided that the uniform distribution is given on this class and $n,N\to\infty$, we describe the asymptotic behaviour of the mathematical expectation and variance and prove Poisson and local normal limit theorems for the random variable equal to the number of blocks of a given size in a partition chosen at random. We find asymptotic expansions of the number of partitions of a set of $n$ elements into $N$ blocks with exactly $k=k(n,N)$ blocks of a given size. 
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A. N. Timashev. Random partitions of sets with a known number of blocks. Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 138-148. http://geodesic.mathdoc.fr/item/DM_2003_15_2_a11/

[1] Sachkov V. N., Kombinatornye metody diskretnoi matematiki, Nauka, Moskva, 1977

[2] Kolchin V. F., “Odin klass predelnykh teorem dlya uslovnykh raspredelenii”, Litov. matem. sb., 8:1 (1968), 53–63 | MR | Zbl

[3] Sachkov V. N., Veroyatnostnye metody v kombinatornom analize, Nauka, Moskva, 1978 | MR | Zbl

[4] Sachkov V. N., “Sluchainye razbieniya mnozhestv s pomechennymi podmnozhestvami”, Matem. sb., 92:3 (1973), 491–502 | Zbl

[5] Sachkov V. N., “Sluchainye razbieniya mnozhestv”, Teoriya veroyatnostei i ee primeneniya, 19:1 (1974), 187–194 | MR | Zbl

[6] Sachkov V. N., “Sluchainye razbieniya mnozhestv”, Matem. voprosy kibern., 8 (1999), 33–54 | MR | Zbl

[7] Arratia R., Tavare S., “Independent process approximations for random combinatiorial structures”, Adv. Math., 104 (1994), 90–154 | DOI | MR | Zbl

[8] Pittel B., “Random set partitions: asymptotic of subset counts”, J. Comb. Theory, 79 (1997), 326–359 | DOI | MR | Zbl

[9] Mutafchiev L., “Limiting distributions for the number of distinct component sizes in relational structures”, J. Comb. Theory, 79 (1997), 1–35 | DOI | MR | Zbl

[10] Kolchin A. V., “Random partitions of a set and the generalised allocation scheme”, Probabilistic Methods in Discrete Mathematics, VSP, Utrecht, 2002, 215–218

[11] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, Moskva, 1976 | MR | Zbl

[12] Riordan Dzh., Vvedenie v kombinatornyi analiz, IL, Moskva, 1962

[13] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, Moskva, 1972 | MR

[14] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Fizmatlit, Moskva, 1962 | MR

[15] Medvedev Yu. I., Ivchenko G. I., “Asimptoticheskie predstavleniya konechnykh raznostei ot stepennoi funktsii v proizvolnoi tochke”, Teoriya veroyatnostei i ee primeneniya, 10:1 (1965), 151–156

[16] Good I. J., “An asymptotic formula for the differences of the powers at zero”, Ann. Math. Statist., 32 (1961), 249–256 | DOI | MR | Zbl

[17] Hsu L. C., “Note on an asymptotic expansion of the $n$th difference of zero”, Ann. Math. Statist., 19:2 (1948), 273–277 | DOI | MR | Zbl

[18] Fedoryuk M. V., Asimptotika. Integraly i ryady, Nauka, Moskva, 1987 | MR