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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

6 Issues per year


CiteScore 2016: 0.16

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.552

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1569-3929
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Volume 17, Issue 1

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Limit theorems for the number of solutions of a system of random linear equations belonging to a given set

V. G. Mikhailov
Published Online: 2007-05-16 | DOI: https://doi.org/10.1515/DMA.2007.003

We investigate the asymptotic behaviour of the distribution of the number ξ(B) of the solutions of a system of homogeneous random linear equations Ax = 0 (the T × n matrix A is composed of independent random variables a i,j uniformly distributed on a set of elements of a finite field K) which belong to some given set B of non-zero n-dimensional vectors over the field K. We consider the case where, under a concordant growth of the parameters n, T → ∞ and variations of the sets B 1, . . . ,Bs such that the mean values converge to finite limits, the limit distribution of the vector (ξ(B 1), ... , ξ(Bs )) is an s-dimensional compound Poisson distribution. We give sufficient conditions for this convergence and find parameters of the limit distribution. We consider in detail the special case where Bk is the set of vectors which do not contain a certain element kK.

About the article

Published Online: 2007-05-16

Published in Print: 2007-04-19


Citation Information: Discrete Mathematics and Applications dma, Volume 17, Issue 1, Pages 13–22, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/DMA.2007.003.

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[1]
V. A. Kopyttsev and V. G. Mikhailov
Discrete Mathematics and Applications, 2010, Volume 20, Number 2

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