FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 511-523

A. N. Veligura

Abstract

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A class of polynomially solvable systems of
```$m$ linear
equations of $n$
$k$ -valued variables
is described. The exact and asymptotic formulae for the cardinal number
$\nu_k(n,m)$ of the class are presented.
In particular, if $n,m\to \infty$ so that $m/n=(1-1/k)+\omega
n^{-1/2}$ , where $\omega \to +\infty$ almost all of such systems with columns
in general position are polynomially solvable.

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Last modified: June 17, 1998