Abstract
Let šn be a semigroup of mappings of a set X with n elements into itself, A be some fixed subset of the set N of natural numbers, and Vn(A) be a set of mappings from šn, with lengths of cycles belonging to A. The mappings from Vn(A) are called A-mappings. We suppose that the set A has an asymptotic density ϱ > 0, and that |k : k ⤠n, k ā A, m ā k ā A|/n ā ϱ2 as n ā ā uniformly over m ā [n, Cn] for each constant C > 1. A number M(α) of different elements in a set {α, α2, α3, ā¦} is called an order of mapping α ā šn. Consider a random mapping Ļ = Ļn(A) having uniform distribution on Vn(A). In the present paper it is shown that random variable ln M(Ļn(A)) is asymptotically normal with mean
Originally published in Diskretnaya Matematika (2017) 29, ā1, 136ā155 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 14-01-00318
Funding statement: This study was supported by the Russian Foundation for Basic Research, grant 14-01-00318.
References
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Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
- Limit theorems for the logarithm of the order of a random A-mapping
Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
- Limit theorems for the logarithm of the order of a random A-mapping