|
Title:
|
On the number of monochromatic solutions of integer linear systems on Abelian groups
|
|
Author:
|
Serra Albó, Oriol; Vena, Lluis
|
|
Other authors:
|
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
|
Abstract:
|
Let G be a finite cyclic group an let r be a positive integer. Let A be a k×m matrix with integer entries. We show that, if A satisfies some natural conditions, then the homogeneous linear system Ax=0 has Ω(|GN|m−k) monochromatic solutions for each r-coloring of GN\{0} and sufficiently large N. Density versions of this counting result are also addressed. |
|
Abstract:
|
Peer Reviewed |
|
Subject(s):
|
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
-Abelian groups
-Algebra
-Arithmetic Ramsey Theory
-Linear systems
-Monochromatic solutions
-Grups abelians
-Àlgebra |
|
Rights:
|
|
|
Document type:
|
Article - Published version
Article |
|
Share:
|
|
