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
Recommended Citation
Palsson, Eyvindur, Steven Senger, and Adam Sheffer. "On the number of discrete chains." Proceedings of the American Mathematical Society 149, no. 12 (2021): 5347-5358.
Journal Title
Proceedings of the American Mathematical Society
COinS
