Counting configuration-free sets in groups
Combinatorics
2016-02-08 v1
Abstract
We provide new examples of the asymptotic counting for the number of subsets on groups of given size which are free of certain configurations. These examples 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. As a consequence, random counterparts are presented as well.
Keywords
Cite
@article{arxiv.1602.01992,
title = {Counting configuration-free sets in groups},
author = {Juanjo Rué and Oriol Serra and Lluís Vena},
journal= {arXiv preprint arXiv:1602.01992},
year = {2016}
}
Comments
31 pages