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Can I read Asymptotic Expansions for the Distribution of the Number of Components in Random Mappings and Partitions on EtoBox?
Asymptotic Expansions for the Distribution of the Number of Components in Random Mappings and Partitions by A. N. Timashov is a Computer Science article available to read on EtoBox.
What is Asymptotic Expansions for the Distribution of the Number of Components in Random Mappings and Partitions about?
We consider the class of all n n single-valued mappings of an n-element set into itself. Assuming that all such mappings have the same probabilities equal to n n , we investigate the distribution of the random variable n equal to the number of connected components in such random mapping. We obtain asymptotic estimates of the probability Pf n D N g as n; N ! 1 in such a way that the ratio N= ln n does not tend to 0 and infinity. In the case where N D 1 2 ln n D o.ln n/ as n ! 1, we obtain a complete asymptotic expansion of this probability. A similar expansion is obtained for the probability Pf n D N g, where n is the random variable equal to the number of cycles in a permutation randomly and equiprobably chosen from the set of all nŠ permutations of degree n, and also for the probability Pf n D N g, where n is the number of blocks in a random partition of a set with n elements.
Who reads Asymptotic Expansions for the Distribution of the Number of Components in Random Mappings and Partitions?
It is typically read by researchers, students, and practitioners in Computer Science.
- Author
- A. N. Timashov
- Publisher
- Walter de Gruyter GmbH
- Published
- 2011
- Language
- EN
- Field
- Computer Science (Physical Sciences)