Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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.
Язык оригинала | английский |
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Страницы (с-по) | 727-740 |
Число страниц | 14 |
Журнал | Journal of Mathematical Sciences (United States) |
Том | 229 |
Номер выпуска | 6 |
DOI | |
Состояние | Опубликовано - мар 2018 |
ID: 15492208