On Erdős Chains in the Plane

Jonathan Passant

Let $P$ be a finite point set in ${\mathbb{R}}^2$ with the set of distance $n$-chains defined as $${\Delta }_n(P)=\{(|p_1-p_2|,|p_2-p_3|,\dots ,|p_n-p_{n+1}|):p_i\in P\}.$$ We show that fo…