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On the number of A-mappings

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Suppose that \( \mathfrak{S} \) n is the semigroup of mappings of the set of n elements into itself, A is a fixed subset of the set of natural numbers ℕ, and V n (A) is the set of mappings from \( \mathfrak{S} \) n whose contours are of sizes belonging to A. Mappings from V n (A) are usually called A-mappings. Consider a random mapping σ n , uniformly distributed on V n(A). Suppose that ν n is the number of components and λ n is the number of cyclic points of the random mapping σ n . In this paper, for a particular class of sets A, we obtain the asymptotics of the number of elements of the set V n (A) and prove limit theorems for the random variables ν n and λ n as n → ∞.

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Correspondence to A. L. Yakymiv.

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Original Russian Text © A. L. Yakymiv, 2009, published in Matematicheskie Zametki, 2009, Vol. 86, No. 1, pp. 139–147.

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Yakymiv, A.L. On the number of A-mappings. Math Notes 86, 132–139 (2009). https://doi.org/10.1134/S0001434609070128

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