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B.A. Sevastyanov

Some classes of random mappings of finite sets and non-homogeneous branching processes

Let be a finite set, where X_t , t = 1, 2, . . . , T, are pairwise nonoverlapping sets, N_t = |X_t| be the cardinality of the set X_t, t = 0, 1, . . . , T. Let ?₁ be the class of all mappings f of the set X′ = X X₀ into X such that the image y = f (x) ∈ X_t?1 ∪ X_t for any x ∈ X_t , t = 1, . . . , T. The cardinality of the set of all mappings of the class ?₁ is . With the use of non-homogeneous branching processes, we study some asymptotical properties of the uniformly distributed on ?₁ random mapping f as N_t → ∞, t = 1, 2, . . . , T. Similar results are obtained for some other classes of random mappings f of the set X.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 14, 01/2004
Pages: 7 - 12

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