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Title:
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On the number of solutions of regular systems in sets with positive density in abelian groups
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Author:
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Král, Daniel; Serra Albó, Oriol; Vena, Lluis
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
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Abstract:
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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. |
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Subject(s):
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-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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Rights:
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Document type:
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Article - Published version
Conference Object |
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