Counting configuration-free sets in groups

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...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 66; pp. 281 - 307
Main Authors Rué, Juanjo, Serra, Oriol, Vena, Lluis
Format Journal Article Publication
LanguageEnglish
Published Elsevier Ltd 01.12.2017
Subjects
Anàlisi numèrica
Elements finits, Mètode dels
Finite element method
Matemàtiques i estadística
Mètodes en elements finits
Àrees temàtiques de la UPC
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Summary: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.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2017.06.027