A Combinatorial Proof of the Effective Nullstellensatz

Let I be an ideal in the affine multi-variate polynomial ring A = K[x1,…,xn]. Beginning with the work of Brownawell, there has been renewed interest in recent years in using the degrees of polynomials which generate I to bound the degree D such that: . This paper will prove the degree bound D using only counting arguments for the ideal I. This provides the first combinatorial proof of the effective Nullstellensatz.