On the number of solutions of regular systems in sets with positive density in abelian groups
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Document typeConference report
Defense date2010
Rights accessRestricted access - publisher's policy
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.
CitationKrál, 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.
ISBN978-84-693-3063-0
Publisher versionhttp://www.jmda2010.unican.es/Librodeactas.pdf
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