Some extensions of Alon's Nullstellensatz

Autor:	Kós, Géza, Mészáros, Tamás, Rónyai, Lajos
Rok vydání:	2011
Předmět:	Mathematics - Combinatorics Mathematics - Commutative Algebra 05-XX 05E40 12D10
Druh dokumentu:	Working Paper
Popis:	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 F\"uredi on hyperplane coverings of discrete cubes. Comment: Inital submission: Thu, 24 Mar 2011
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1103.4768 Zobrazit plný text záznamu View this record from Arxiv