2011/03/24 by Géza Kós, Tamás Mészáros, Kós, Géza +3
Mathematics · #05-XX #05E40 #12D10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:05-XX #msc:05E40 #msc:12D10
paper · pdf · doi:10.48550/arxiv.1103.4768
Inital submission: Thu, 24 Mar 2011
arxiv created 2011/08/15 · arxiv updated 2011/08/16
Alon's combinatorial Nullstellensatz, and in particular the resulting nonvanishing criterion is one of the most powerful algebraic tools in combinatorics, with many important applications. In this paper we extend the nonvanishing theorem in two directions. We prove a version allowing multiple points. Also, we establish a variant which is valid over arbitrary commutative rings, not merely over subrings of fields. As an application, we prove extensions of the theorem of Alon and Füredi on hyperplane coverings of discrete cubes.