Loading...
Loading...

Go to the content (press return)

On the number of solutions of regular systems in sets with positive density in abelian groups

Author
Král, D.; Serra, O.; Vena, L.
Type of activity
Presentation of work at congresses
Name of edition
VII Jornadas de Matemática Discreta y Algorítmica
Date of publication
2010
Presentation's date
2010-06-16
Book of congress proceedings
VII Jornadas Matemática Discreta y Algorítmica : libro de actas
First page
401
Last page
409
Repository
http://hdl.handle.net/2117/11261 Open in new window
URL
http://www.jmda2010.unican.es/Librodeactas.pdf Open in new window
Abstract
We prove a density version for the Ramsey statement that, for fixed r and sufficiently large n, every coloring of an abelian group of order n with r colors has nontrivial monochromatic solutions of the system Ax = 0, where A is an integer matrix with row–sum zero. Our result shows that asymptotically the number of solutions is in fact as large as it can be expected.
Citation
Král, D.; Serra, O.; Vena, L. On the number of solutions of regular systems in sets with positive density in abelian groups. A: VII Jornadas de Matemática Discreta y Algorítmica. "VII Jornadas de Matemática Discreta y Algorítmica". Castro Urdiales: 2010, p. 401-409.
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants

  • Král, Daniel  (author and speaker )
  • Serra Albo, Oriol  (author and speaker )
  • Vena Cros, Lluis  (author and speaker )