The combinatorial Nullstellensatz

The “combinatorial Nullstellensatz” is a relatively elementary statement due to Noga Alon (1999) whose name, while possibly frightening, really says what it is and what it is good for. (A freely available version is there .) Nullstellensatz is the classic name for a theorem of David Hilbert that relates loci in $F^n$ defined by polynomial equations and the ideals of the polynomial ring…