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Some classes of random mappings of finite sets and non-homogeneous branching processes
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B.A. Sevastyanov
Published/Copyright:
January 1, 2004
Let 
be a finite set, where Xt , t = 1, 2, . . . , T, are pairwise nonoverlapping sets, Nt = |Xt| be the cardinality of the set Xt, t = 0, 1, . . . , T. Let ℱ1 be the class of all mappings f of the set X′ = X \ X0 into X such that the image y = f (x) ∈ Xt−1 ∪ Xt for any x ∈ Xt ,
t = 1, . . . , T. The cardinality of the set of all mappings of the class ℱ1 is 
. With the use of non-homogeneous branching processes, we study some asymptotical properties of the uniformly distributed on ℱ1 random mapping f as Nt → ∞, t = 1, 2, . . . , T. Similar results are
obtained for some other classes of random mappings f of the set X.
Published Online: 2004-01-01
Published in Print: 2004-01-01
Copyright 2004, Walter de Gruyter
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Articles in the same Issue
- Andrei Andreevich Markov (to the centenary of the birth)
- Some classes of random mappings of finite sets and non-homogeneous branching processes
- The method of boundary functionals for non-regular structures
- A formula for the radius of stability of a vector l∞-extremal trajectory problem
- Solving systems of polynomial equations over Galois–Eisenstein rings with the use of the canonical generating systems of polynomial ideals
- Standard basis of a polynomial ideal over commutative Artinian chain ring
- On some systems of generators of symmetric and alternating groups which allow a simple software implementation
