@article{MVK_2019_10_3_a0,
author = {V. E. Viktorenkov},
title = {Cycle structure of random permutations on the set of two-color elements. {I}},
journal = {Matemati\v{c}eskie voprosy kriptografii},
pages = {9--32},
year = {2019},
volume = {10},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MVK_2019_10_3_a0/}
}
V. E. Viktorenkov. Cycle structure of random permutations on the set of two-color elements. I. Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 3, pp. 9-32. http://geodesic.mathdoc.fr/item/MVK_2019_10_3_a0/
[1] Sachkov V. N., Veroyatnostnye metody v kombinatornom analize, Nauka, M., 1978, 288 pp.
[2] Sachkov V. N., “Operator redutsirovaniya. I”, Trudy po diskretnoi matematike, 2 (1998), 282–295 | MR | Zbl
[3] Sachkov V. N., “Operator redutsirovaniya i preobrazovaniya so svoistvami nasledstvennosti, ch. II”, Trudy po diskretnoi matematike, 10 (2007), 269–286
[4] Sachkov V. N., “Sluchainye podstanovki s transformirovannymi tsiklami”, Matematicheskie voprosy kriptografii, 3:4 (2012), 127–150 | DOI | MR
[5] Sachkov V. N., “Sluchainye podstanovki s tsiklami ogranichennoi dliny i transformirovaniem”, Matematicheskie voprosy kriptografii, 5:3 (2014), 117–136 | DOI | MR
[6] Ivchenko G. I., Medvedev Yu. I., “Metod V. L. Goncharova i ego razvitie v analize razlichnykh modelei sluchainykh podstanovok”, Teoriya veroyatnostei i ee primeneniya, 47:3 (2002), 558–566 | DOI | Zbl
[7] Ivchenko G. I., Medvedev Yu. I., “Ob odnom klasse neravnoveroyatnykh podstanovok sluchainoi stepeni”, Trudy po diskretnoi matematike, 7 (2003), 75–88
[8] Ivchenko G. I., Medvedev Yu. I., “Sluchainye nepolnye podstanovki”, Trudy po diskretnoi matematike, 11 (2008), 35–46
[9] Ivchenko G. I., Medvedev Yu. I., Diskretnye raspredeleniya. Veroyatnostno-statisticheskii spravochnik. Mnogomernye raspredeleniya, LENAND, M., 2016, 336 pp.
[10] Viktorenkov V. E., “Orgraf polinomialnogo preobrazovaniya nad kommutativnym lokalnym koltsom”, Obozr. prikl. i promyshl. matem., 7:2 (2000), 327
[11] Viktorenkov V. E., “Ob asimptoticheskoi normalnosti logarifma poryadka sluchainoi polinomialnoi podstanovki nad primarnym koltsom vychetov s ogranichennoi razryadnostyu”, Obozr. prikl. i promyshl. matem., 7:2, 486 | MR
[12] Viktorenkov V. E., “Ob'emy tsiklov sluchainykh polinomialnykh preobrazovanii kolets”, Obozr. prikl. i promyshl. matem., 9:2 (2002), 347–348 | MR
[13] Viktorenkov V. E., “O nekotorykh kharakteristikakh tsiklovoi struktury sluchainykh ravnoveroyatnykh podstanovok s pomechennymi tsiklami i ikh primenenie dlya issledovaniya polinomialnykh preobrazovanii kolets”, Obozr. prikl. i promyshl. matem., 10:3 (2003), 621
[14] Viktorenkov V. E., “O stroenii polinomialnykh preobrazovanii nad konechnymi kommutativnymi koltsami s edinitsei”, Diskretnaya matematika, 29:3 (2017), 3–23 | DOI
[15] Larin M. V., “Tranzitivnye polinomialnye preobrazovaniya kolets vychetov”, Diskretnaya matematika, 14:2 (2002), 20–32 | DOI | Zbl
[16] Ermilov D. M., Kozlitin O. A., “Tsiklovaya struktura polinomialnogo generatora nad koltsom Galua”, Matematicheskie voprosy kriptografii, 4:1 (2013), 27–57 | DOI
[17] Ermilov D. M., Kozlitin O. A., “O stroenii grafa polinomialnogo preobrazovaniya koltsa Galua”, Matematicheskie voprosy kriptografii, 3:6 (2015), 47–73 | DOI | MR
[18] Kozlitin O. A., “Otsenka dliny maksimalnogo tsikla v grafe polinomialnogo preobrazovaniya koltsa Galua – Eizenshteina”, Diskretnaya matematika, 29:4 (2017), 41–58 | DOI
[19] 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 | MR | Zbl
[20] Kolchin V. F., Sluchainye otobrazheniya, Nauka, M., 1984, 206 pp.
[21] Anashin V. S., “Uniformly distributed sequences in computer algebra or how construct program generators of random numbers”, J. Math. Sci., 8 (1999), 193–208 | MR
[22] Arratia R., Barbour A. D., Tavaré S., “On Poisson-Dirichlet limits for random decomposable combinatorial structures”, Comb., Probab. and Comput., 8 (1999), 193–208 | DOI | MR | Zbl
[23] Hansen J. C., “Order statistics for decomposable combinatorial structures”, Random Structures Algorithms, 5:4 (1994), 517–533 | DOI | MR | Zbl
[24] Shepp L. A., Lloyd S. P., “Ordered cycle lengths in random permutations”, Trans. Amer. Math. Soc., 121:21 (1966), 340–357 | DOI | MR | Zbl