Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777371 | European Journal of Combinatorics | 2017 | 27 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Juanjo Rué, Oriol Serra, Lluis Vena,