The Multivariate Schwartz--Zippel Lemma
The Multivariate Schwartz--Zippel Lemma
Motivated by applications in combinatorial geometry, we consider the following question: Let $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_m)$ be an $m$-partition of a positive integer $n$, $S_i \subseteq \mathbb{C}^{\lambda_i}$ be finite sets, and let $S:=S_1 \times S_2 \times \cdots \times S_m \subset \mathbb{C}^n$ be the multigrid defined by $S_i$. Suppose $p$ is an $n$-variate degree …