Counting configuration-free sets in groups

© 2017 Elsevier Ltd. We provide asymptotic counting for the number of subsets of given size which are free of certain configurations in finite groups. Applications include sets without solutions to equations in non-abelian groups, and linear configurations in abelian groups defined from group homomo...

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Detalles Bibliográficos
Autores: Rué Perna, Juan José|||0000-0002-6420-3179, Serra Albó, Oriol|||0000-0001-8561-4631, Vena Cros, Lluís|||0000-0002-0075-3673
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/111650
Acceso en línea:https://hdl.handle.net/2117/111650
https://dx.doi.org/10.1016/j.ejc.2017.06.027
Access Level:acceso abierto
Palabra clave:Finite element method
Elements finits, Mètode dels
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Descripción
Sumario:© 2017 Elsevier Ltd. We provide asymptotic counting for the number of subsets of given size which are free of certain configurations in finite groups. Applications include sets without solutions to equations in non-abelian groups, and linear configurations in abelian groups defined from group homomorphisms. The results are obtained by combining the methodology of hypergraph containers joint with arithmetic removal lemmas. Random sparse versions and threshold probabilities for existence of configurations in sets of given density are presented as well.