The number of roots of a polynomial system

Abstract

Let $I$ be a zero-dimensional ideal in the polynomial ring $K[x_1, \ldots , x_n]$ over a field $K$. In this paper we give a bound for the number of roots of $I$ in $K^n$ counted with combinatorial multiplicity. As consequence we give a proof of the Alon’s combinatorial nullstellensatz. http://dx.doi.org/10.1017/S000497271200033