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On Random Partitions Induced by Random Maps. / Krachun, D.; Yakubovich, Yu.

в: Journal of Mathematical Sciences (United States), Том 229, № 6, 03.2018, стр. 727-740.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Krachun, D & Yakubovich, Y 2018, 'On Random Partitions Induced by Random Maps', Journal of Mathematical Sciences (United States), Том. 229, № 6, стр. 727-740. https://doi.org/10.1007/s10958-018-3712-5

APA

Krachun, D., & Yakubovich, Y. (2018). On Random Partitions Induced by Random Maps. Journal of Mathematical Sciences (United States), 229(6), 727-740. https://doi.org/10.1007/s10958-018-3712-5

Vancouver

Krachun D, Yakubovich Y. On Random Partitions Induced by Random Maps. Journal of Mathematical Sciences (United States). 2018 Март;229(6):727-740. https://doi.org/10.1007/s10958-018-3712-5

Author

Krachun, D. ; Yakubovich, Yu. / On Random Partitions Induced by Random Maps. в: Journal of Mathematical Sciences (United States). 2018 ; Том 229, № 6. стр. 727-740.

BibTeX

@article{34405f2c2a064a4784f1858277610e35,
title = "On Random Partitions Induced by Random Maps",
abstract = "The partition lattice of the set [n] with respect to refinement is studied. Any map ϕ: [n] → [n], is associated with a partition of [n] by taking preimages of the elements. Assume that t partitions p1, p2, . . . , pt are chosen independently according to the uniform measure on the set of mappings [n] → [n]. It is shown that the probability for the coarsest refinement of all the partitions pi to be the finest partition {{1}, . . . , {n}} tends to 1 for any t ≥ 3 and to e−1/2 for t = 2. It is also proved that the probability for the finest coarsening of the partitions pi to be the one-block partition tends to 1 as t(n) − log n→∞ and tends to 0 as t(n) − log n→−∞. The size of the maximal block of the finest coarsening of all the pi for a fixed t is also studied.",
author = "D. Krachun and Yu. Yakubovich",
note = "Krachun, D., Yakubovich, Y. On Random Partitions Induced by Random Maps. J Math Sci 229, 727–740 (2018). https://doi.org/10.1007/s10958-018-3712-5",
year = "2018",
month = mar,
doi = "10.1007/s10958-018-3712-5",
language = "English",
volume = "229",
pages = "727--740",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - On Random Partitions Induced by Random Maps

AU - Krachun, D.

AU - Yakubovich, Yu.

N1 - Krachun, D., Yakubovich, Y. On Random Partitions Induced by Random Maps. J Math Sci 229, 727–740 (2018). https://doi.org/10.1007/s10958-018-3712-5

PY - 2018/3

Y1 - 2018/3

N2 - The partition lattice of the set [n] with respect to refinement is studied. Any map ϕ: [n] → [n], is associated with a partition of [n] by taking preimages of the elements. Assume that t partitions p1, p2, . . . , pt are chosen independently according to the uniform measure on the set of mappings [n] → [n]. It is shown that the probability for the coarsest refinement of all the partitions pi to be the finest partition {{1}, . . . , {n}} tends to 1 for any t ≥ 3 and to e−1/2 for t = 2. It is also proved that the probability for the finest coarsening of the partitions pi to be the one-block partition tends to 1 as t(n) − log n→∞ and tends to 0 as t(n) − log n→−∞. The size of the maximal block of the finest coarsening of all the pi for a fixed t is also studied.

AB - The partition lattice of the set [n] with respect to refinement is studied. Any map ϕ: [n] → [n], is associated with a partition of [n] by taking preimages of the elements. Assume that t partitions p1, p2, . . . , pt are chosen independently according to the uniform measure on the set of mappings [n] → [n]. It is shown that the probability for the coarsest refinement of all the partitions pi to be the finest partition {{1}, . . . , {n}} tends to 1 for any t ≥ 3 and to e−1/2 for t = 2. It is also proved that the probability for the finest coarsening of the partitions pi to be the one-block partition tends to 1 as t(n) − log n→∞ and tends to 0 as t(n) − log n→−∞. The size of the maximal block of the finest coarsening of all the pi for a fixed t is also studied.

UR - http://www.scopus.com/inward/record.url?scp=85042357942&partnerID=8YFLogxK

U2 - 10.1007/s10958-018-3712-5

DO - 10.1007/s10958-018-3712-5

M3 - Article

AN - SCOPUS:85042357942

VL - 229

SP - 727

EP - 740

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 15492208