Some extensions of Alon's Nullstellensatz

Géza Kós, Tamás Mészáros, L. Rónyai

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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. The nonvanishing theorem has been extended in two directions. The first and the third named authors proved a version allowing multiple points. Michałek established a variant which is valid over arbitrary commutative rings, not merely over subrings of fields. In this paper we give new proofs of the latter two results and provide a common generalization of them. As an application, we prove extensions of the theorem of Alon and Füredi on hyperplane coverings of discrete cubes.

Original languageEnglish
Pages (from-to)507-519
Number of pages13
JournalPublicationes Mathematicae
Volume79
Issue number3-4
DOIs
Publication statusPublished - 2011

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Subring
Combinatorics
Theorem
Commutative Ring
Hyperplane
Regular hexahedron
Covering
Valid
Arbitrary
Generalization

Keywords

  • Combinatorial Nullstellensatz
  • Covering by hyperplanes
  • Interpolation
  • Multiple point
  • Multiset
  • Polynomial method
  • Zero divisor

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Some extensions of Alon's Nullstellensatz. / Kós, Géza; Mészáros, Tamás; Rónyai, L.

In: Publicationes Mathematicae, Vol. 79, No. 3-4, 2011, p. 507-519.

Research output: Contribution to journalArticle

Kós, Géza ; Mészáros, Tamás ; Rónyai, L. / Some extensions of Alon's Nullstellensatz. In: Publicationes Mathematicae. 2011 ; Vol. 79, No. 3-4. pp. 507-519.
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