On the number of discrete chains

Abstract

We study a generalization of the Erdos unit distance problem to chains of k distances. Given P, a set of n points, and a sequence of distances (δ1, . . . , δk), we study the maximum possible number of tuples of distinct points (p1, . . . , pk+1) ϵ Pk+1 satisfying |pjpj+1| = δj for every 1 ≤ j ≤ k. We study the problem in R2 and in R3, and derive upper and lower bounds for this family of problems.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1090/proc/15603

Publication Date

1-1-2021

Journal Title

Proceedings of the American Mathematical Society

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