Asymptotic density of rational sets in free abelian groups

Abstract

In this paper we study asymptotic density of rational sets in free abelian group ${\mathbb{Z}}^n$ of rank $n$. We show that any rational set $R$ in ${\mathbb{Z}}^n$ has asymptotic density. If $R$ is given by its semi-simple decomposition we show how to compute its asymptotic density.

6 pages, added references, generalized for densities induced by any p-norm

Cited by in corpus (1)

• On systems of equations in free abelian groups