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
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 k ∈ K.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.