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On the number of cyclic points of random A-mapping
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A. L. Yakymiv
Published/Copyright:
May 1, 2014
Abstract
Let Sn be the semigroup of mappings of the set of n elements into itself, A be a fixed subset of the set of natural numbers ℕ, and Vn(A) be the set of mappings from Sn with cycle lengths belonging to A. Mappings from Vn(A) are called A-mappings. Consider a random mapping σn uniformly distributed on Vn(A). Let λn be the number of cyclic points of σn. It is supposed that the set A has an asymptotic nonnegative density ς. We describe the asymptotic behaviour of the cardinality of the set Vn(A) and prove a limit theorem for the sequence of random variables λn as n → ∞.
Keywords : random A-mappings; random A-permutations; cyclic points; cycles; trees; components of random permutations; Abel transform; Tauberian theorem; Abelian theorem
Published Online: 2014-5-1
Published in Print: 2013-12-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
Keywords for this article
random A-mappings;
random A-permutations;
cyclic points;
cycles;
trees;
components of random permutations;
Abel transform;
Tauberian theorem;
Abelian theorem
Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
