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On the probability of coincidence of cycle lengths for independent random permutations with given number of cycles
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Aleksandr N. Timashev
Published/Copyright:
December 8, 2015
Abstract
From the set of all permutations of the degree n with a given number N ≤ n of cycles two permutations are choosed randomly, uniformly and independently. The cycles of each permutation are numbered in some of N! possible ways. We study the coincidence probability of the cycle lengths of permutations for a given numbering. This probability up to a suitably selected renumbering of cycles of the first permutation equals to the probability of similarity of these permutations. The asymptotic estimates of the coincidence probability of the cycle lengths are obtained for five types of relations between N, n → ∞.
Keywords : coincidence probability; cycle lengths; random permutations; generalized scheme of random allocations; Stirling numbers of the first kind
Received: 2014-4-1
Published Online: 2015-12-8
Published in Print: 2015-12-1
© 2015 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Cardinality estimates for some classes of regular languages
- On large deviations of a branching process in random environments with immigration at moments of extinction
- Existence of arbitrarily long square-free words with one possible mismatch
- On frequencies of elements in multicyclic random sequence modulo 4
- Single tests for logical gates
- On the probability of coincidence of cycle lengths for independent random permutations with given number of cycles
Keywords for this article
coincidence probability;
cycle lengths;
random permutations;
generalized scheme of random allocations;
Stirling numbers of the first kind
Articles in the same Issue
- Frontmatter
- Cardinality estimates for some classes of regular languages
- On large deviations of a branching process in random environments with immigration at moments of extinction
- Existence of arbitrarily long square-free words with one possible mismatch
- On frequencies of elements in multicyclic random sequence modulo 4
- Single tests for logical gates
- On the probability of coincidence of cycle lengths for independent random permutations with given number of cycles
