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On the number of solutions of regular systems in sets with positive density in abelian groups
Král, Daniel; Serra Albó, Oriol; Vena, Lluis
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
Abelian groups
Hypergraphs
Group theory
Grups abelians
Grafs, Teoria de
Grups, Teoria de
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