The largest $(k, \ell)$-sum-free sets in compact abelian groups

15 Jan 2019 Kravitz Noah

A subset $A$ of a finite abelian group is called $(k,\ell)$-sum-free if $kA \cap \ell A=\emptyset.$ In this paper, we extend this concept to compact abelian groups and study the question of how large a measurable $(k,\ell)$-sum-free set can be. For integers $1 \leq k <\ell$ and a compact abelian group $G$, let $$\lambda_{k,\ell}(G)=\sup\{ \mu(A): kA \cap \ell A =\emptyset \}$$ be the maximum possible size of a $(k,\ell)$-sum-free subset of $G$... (read more)

PDF Abstract
No code implementations yet. Submit your code now

Categories


  • COMBINATORICS
  • GROUP THEORY
  • NUMBER THEORY