Geodesic
Parametric models of $r$-permutations and $r$-partitions and their probabilistic-statistical analysis
Matematičeskie voprosy kriptografii, Tome 9 (2018) no. 1, pp. 47-64 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Some problems of the probabilistic combinatorics are investigated when some parametric probabilistic measure on the set of combinatorial objects under consideration is given. Analysis of $r$-permutations and $r$-partitions of finite sets in an one-parametric model is performed. 
@article{MVK_2018_9_1_a2,
     author = {G. I. Ivchenko and Yu. I. Medvedev},
     title = {Parametric models of $r$-permutations and $r$-partitions and their probabilistic-statistical analysis},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {47--64},
     year = {2018},
     volume = {9},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a2/}
}
TY  - JOUR
AU  - G. I. Ivchenko
AU  - Yu. I. Medvedev
TI  - Parametric models of $r$-permutations and $r$-partitions and their probabilistic-statistical analysis
JO  - Matematičeskie voprosy kriptografii
PY  - 2018
SP  - 47
EP  - 64
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a2/
LA  - ru
ID  - MVK_2018_9_1_a2
ER  - 
%0 Journal Article
%A G. I. Ivchenko
%A Yu. I. Medvedev
%T Parametric models of $r$-permutations and $r$-partitions and their probabilistic-statistical analysis
%J Matematičeskie voprosy kriptografii
%D 2018
%P 47-64
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a2/
%G ru
%F MVK_2018_9_1_a2
G. I. Ivchenko; Yu. I. Medvedev. Parametric models of $r$-permutations and $r$-partitions and their probabilistic-statistical analysis. Matematičeskie voprosy kriptografii, Tome 9 (2018) no. 1, pp. 47-64. http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a2/

[1] de Brein N. G., Asimptoticheskie metody v analize, IL, M., 1961, 248 pp.

[2] Vatutin V. A., Mikhailov V. G., “Predelnye teoremy dlya chisla pustykh yacheek v ravnoveroyatnoi skheme razmescheniya chastits komplektami”, Teoriya veroyatn. i ee primen., 27:4 (1982), 684–692 | Zbl

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

[4] Ivchenko G. I., Medvedev Yu. I., “O sluchainykh podstanovkakh”, Trudy po diskretnoi matematike, 5 (2002), 73–92

[5] Ivchenko G. I., Medvedev Yu. I., “Metod V. L. Goncharova i ego razvitie v analize razlichnykh modelei sluchainykh podstanovok”, Teoriya veroyatn. i ee primen., 47:3 (2002), 558–566 | DOI | Zbl

[6] Ivchenko G. I., Medvedev Yu. I., “Ob odnom klasse neravnoveroyatnykh podstanovok sluchainoi stepeni”, Trudy po diskretnoi matematike, 7 (2003), 75–88

[7] Ivchenko G. I., Medvedev Yu. I., “Neravnoveroyatnye mery na mnozhestvakh razlozhimykh kombinatornykh ob'ektov”, Obozrenie prikl. i promyshl. matem., 10:2 (2003), 348–349

[8] Ivchenko G. I., Medvedev Yu. I., Sachkov V. N., “Nekotorye problemy veroyatnostnoi kombinatoriki”, Matematika i bezopasnost informatsionnykh tekhnologii, Mater. konf. (MGU, 23.10.2003), MTsNMO, M., 2004, 45–52

[9] Ivchenko G. I., Medvedev Yu. I., “Sluchainye kombinatornye ob'ekty”, Doklady AN, 396:2 (2004), 151–154 | Zbl

[10] Ivchenko G. I., Medvedev Yu. I., “Statistika parametricheskoi modeli sluchainykh podstanovok”, Trudy po diskretnoi matematike, 8 (2004), 116–127

[11] Ivchenko G. I., Medvedev Yu. I., “Statisticheskie vyvody dlya sluchainykh podstanovok po nepolnym dannym”, Trudy po diskretnoi matematike, 9 (2006), 66–76 | Zbl

[12] Ivchenko G. I., Medvedev Yu. I., “Sluchainye podstanovki: obschaya parametricheskaya model”, Diskretnaya matematika, 18:4 (2006), 105–112 | DOI | Zbl

[13] Ivchenko G. I., Medvedev Yu. I., “Sluchainye kombinatornye ob'ekty v obschei parametricheskoi modeli”, Trudy po diskretnoi matematike, 10 (2007), 73–86

[14] Ivchenko G. I., Soboleva M. V., “Nekotorye neravnoveroyatnye modeli sluchainykh podstanovok”, Diskretnaya matematika, 23:3 (2011), 23–31 | DOI

[15] Ivchenko G. I., Medvedev Yu. I., Diskretnye raspredeleniya. Veroyatnostno-statisticheskii spravochnik: Odnomernye raspredeleniya, LENAND, M., 2015, 256 pp.

[16] Ivchenko G. I., Medvedev Yu. I., “Parametricheskie modeli sluchainykh kombinatornykh ob'ektov eksponentsialnogo tipa i voprosy ikh veroyatnostno-statisticheskogo analiza”, Matematicheskie voprosy kriptografii, 8:3 (2017), 41–56 | DOI | Zbl

[17] Sachkov V. N., “Sluchainye razbieniya mnozhestv”, Teoriya veroyatn. i ee primen., 19:1 (1974), 178–194

[18] Sachkov V. N., “Sluchainye razbieniya”, Tr. II Vsesoyuzn. sem. po kombin. matem., v. 1, Voprosy kibernetiki, 16, Sov. radio, M., 1975, 88–94

[19] Sachkov V. N., Kombinatornye metody diskretnoi matematiki, Nauka, M., 1977, 320 pp.

[20] Sachkov V. N., Veroyatnostnye metody v kombinatornom analize, Nauka, M., 1978, 288 pp.

[21] Sachkov V. N., “Sluchainye razbieniya mnozhestv”, Matematicheskie voprosy kibernetiki, 8 (1999), 33–54 | Zbl

[22] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, 2-e izd., MTsNMO, M., 2004, 424 pp.

[23] Bell E. T., “Exponential polynomials”, Ann. Math., 35 (1934), 258–277 | DOI | MR

[24] Broder A. Z., “The $r$-Stirling numbers”, Discrete Math., 49:3 (1984), 241–259 | DOI | MR | Zbl

[25] Sarlitz L., “Weighted Stirling numbers of the first and second kind. I”, Fibonacci Quart., 18 (1980), 147–162 | MR

[26] Corcino C. B., Corcino R. B., “An asymptotic formula for $r$-Bell numbers with real arguments”, ISRN Discrete Mathematics, 2013, 274697, 7 pp. | Zbl

[27] Harper L., “Stirling behavior is asymptotically normal”, Ann. Math. Stat., 38:2 (1961), 410–414 | DOI | MR

[28] Hwang H. K., “On convergence rates in the central limit theorems for combinatorial structures”, Eur. J. Comb., 19:3 (1998), 329–343 | DOI | MR | Zbl

[29] Koutras M., “Non-central Stirling numbers and some applications”, Discrete Math., 42 (1982), 73–89 | DOI | MR | Zbl

[30] Mezö I., “On the maximum of $r$-Stirling numbers”, Adv. Appl. Math., 41:3 (2008), 293–306 | DOI | MR | Zbl