Unit Distance Problems
Daniel Oberlin, Richard Oberlin
TL;DR
This paper investigates the maximum number of unit distance pairs in finite point sets in two and three dimensions, exploring both discrete and continuous variants of Erdős's problem.
Contribution
It provides new bounds and insights into the maximum number of unit distances in finite point configurations in R^2 and R^3.
Findings
Derived new upper bounds for unit distances in R^2 and R^3
Analyzed discrete and continuous variants of Erdős's problem
Identified configurations that maximize unit distances
Abstract
We study some discrete and continuous variants of the following problem of Erdos: given a finite subset P of R^2 or R^3, what is the maximum number of pairs (p_1,p_2) with p_1,p_2 in P and |p_1 -p_2 |=1?
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Taxonomy
TopicsLimits and Structures in Graph Theory · Mathematics and Applications · Advanced Graph Theory Research