Abstract

We study a variant of Erd\H os' unit distance problem, concerning dot products between successive pairs of points chosen from a large finite point set. Specifically, given a large finite set of n points E, and a sequence of nonzero dot products (α1,…,αk), we give upper and lower bounds on the maximum possible number of tuples of distinct points (A1,…,Ak+1)∈Ek+1 satisfying Aj⋅Aj+1=αj for every 1≤j≤k.

Department(s)

Mathematics

Document Type

Article

Keywords

Mathematics - Combinatorics, 51A20, 52C10

Publication Date

9-9-2020

Journal Title

arXiv preprint arXiv

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