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On the number of monochromatic solutions of integer linear systems on Abelian groups

Author
Serra, O.; Vena, L.
Type of activity
Journal article
Journal
Electronic notes in discrete mathematics
Date of publication
2011-12-01
Volume
38
First page
777
Last page
781
DOI
https://doi.org/10.1016/j.endm.2011.10.030 Open in new window
Repository
http://hdl.handle.net/2117/14688 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S157106531100196X Open in new window
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.
Citation
Serra, O.; Vena, L. On the number of monochromatic solutions of integer linear systems on Abelian groups. "Electronic notes in discrete mathematics", 01 Desembre 2011, vol. 38, p. 777-781.
Keywords
Arithmetic Ramsey Theory, Linear systems, Monochromatic solutions
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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