Timashev, Aleksandr N.
Published in
Discrete Mathematics and Applications

We consider a generalized scheme of allocation of n particles (elements) over unordered cells (components) under the condition that the number of particles in each cell belongs to a fixed finite set A of positive integers. A new asymptotic estimates for the total number In(A) of variants of allocations of n particles are obtained under some conditi...

Timashev, Aleksandr N.
Published in
Discrete Mathematics and Applications

We consider problems on the convergence of distributions of the total number of components and numbers of components with given volume to the Poisson law. Sufficient conditions of such convergence are given. Our results generalize known statemets on the limit Poisson laws of the number of components (cycles, unrooted and rooted trees, blocks and ot...

Chickrin, D. E. Chuprunov, A. N. Kokunin, P. A.
Published in
Lobachevskii Journal of Mathematics

In some non-homogeneous generalized allocation schemes we formulate conditions under which the number of given value cells from the first K cells converges to a Poisson random variable. The method of the proofs is founded on some analog of Kolchin formula. As corollary we obtain a Poisson limit theorems for the number of given value cells from the ...

Kolchin, A. V. Bezrodnyy, B. F. Leeva, M. A.
Published in
Moscow University Computational Mathematics and Cybernetics

An example of applying a generalized allocation scheme to studying the asymptotic behavior of combinatorial objects is considered. The allocation of tuples of zeros and ones onto a circle generated by a shift register under certain conditions is analyzed.

Afonina, Aleksandra I. Kayumov, Il’giz R. Chuprunov, Aleksey N.
Published in
Discrete Mathematics and Applications

The article is devoted to the memory of Valentin Fedorovich Kolchin. Let ζ, ζi (i ∈ N) be independent identically distributed nonnegative integer-valued random variables, (ηi1,…, ηiN) be the fillings of cells in the generalized scheme of allocation of ζi particles into N cells, 1 ≤ i ≤ n, for fixed Zn = (ζ1, …, ζn) these allocation schemes are inde...

Pavlov, Yu. L.
Published in
Discrete Mathematics and Applications

The paper is concerned with the generalized scheme of allocation particles to cells with negative binomial distribution of independent random variables. The limit distributions for the largest numbers of particles in a cell and for the number of cells with prescribed number of particles are obtained. This example of the generalized allocation schem...

Chuprunov, A. N. Khamdeev, B. I.
Published in
Russian Mathematics

We consider n messages of N blocks each, where each block is encoded by some antinoise coding method. The method can correct no more than one error. We assume that the number of errors in the ith message belongs to some finite random subset of nonnegative integer numbers. Let A stand for the event that all errors are corrected; we study the probabi...