The Generalized Combinatorial Lason-Alon-Zippel-Schwartz Nullstellensatz Lemma

We survey a few strengthenings and generalizations of the Combinatorial Nullstellensatz of Alon and the Schwartz-Zippel Lemma. These lemmas guarantee the existence of (a certain number of) nonzeros of a multivariate polynomial when the variables run independently through sufficiently large ranges.