Distinct Distances Between a Line and Strip

2025/04/06 by Sanjana Das, Das, Sanjana, Adam Sheffer +1
Business, Management and Accounting · Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Facility Location and Emergency Management #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2504.04594

openalex publication_date 2025/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new type of distinct distances result: a lower bound on the number of distances between points on a line and points on a two-dimensional strip. This can be seen as a generalization of the well-studied problems of distances between points on two lines or curves. Unlike these existing problems, this new variant only makes sense if the points satisfy an additional spacing condition. Our work can also be seen as an exploration of the proximity technique that was recently introduced by Solymosi and Zahl. This technique lies at the heart of our analysis.

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