Angle chains and pinned variants

Abstract

We study a variant of the Erd\H os unit distance problem, concerning angles between successive triples of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, and a sequence of angles $({\alpha }_1,\dots ,{\alpha }_k)$, we give upper and lower bounds on the maximum possible number of tuples of distinct points $(x_1,\dots ,x_{k+2})\in E^{k+2}$ satisfying $\angle (x_j,x_{j+1},x_{j+2})={\alpha }_j$ for every $1\le j\le k$ as well as pinned analogues.

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References in corpus (1)

• Finite Point Configurations and the Regular Value Theorem in a Fractal setting