# This Collection

By Defense Date By Authors By Titles By Subject

# Statistics

View Statistics All RECERCAT

# My RECERCAT

 Title: Punctured combinatorial Nullstellensätze Ball, Simeon Michael; Serra Albó, Oriol Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions In this article we present a punctured version of Alon's Nullstellensatz which states that if $f$ vanishes at nearly all, but not all, of the common zeros of some polynomials $g_1(X_1),\ldots,g_n(X_n)$ then every $I$-residue of $f$, where the ideal $I=\langle g_1,\ldots,g_n\rangle$, has a large degree. Furthermore, we extend Alon's Nullstellensatz to functions which have multiple zeros at the common zeros of $g_1,g_2,\ldots,g_n$ and prove a punctured version of this generalised version. Some applications of these punctured Nullstellens\"atze to projective and affine geometries over an arbitrary field are considered which, in the case that the field is finite, will lead to some bounds related to linear codes containing the all one vector. Combinatorial analysisNullstellensatzPolinomialAnàlisi combinatòriaClassificació AMS::05 CombinatoricsClassificació AMS::51 Geometry Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/ Article

# Related documents

## Other documents of the same author

Ball, Simeon Michael; Gács, Andras
Ball, Simeon Michael; Zieve, Michael
Ball, Simeon Michael; Lavrauw, Michel
Ball, Simeon Michael
Ball, Simeon Michael; Blokhuis, Aart

Coordination

Supporters