FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

On systems of polynomially solvable linear equations with $k$-valued variables

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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Location: http://mech.math.msu.su/~fpm/eng/98/982/98203h.htm
Last modified: June 17, 1998