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Combinatorics of intervals in the plane I: trapezoids
- Publication Year :
- 2020
-
Abstract
- We study arrangements of intervals in $\mathbb{R}^2$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some unexpected examples of sets of intervals forming many trapezoids, where an important role is played by degree 2 curves.<br />Comment: 14 pages, 11 figures
- Subjects :
- Mathematics - Combinatorics
Computer Science - Computational Geometry
52C30, 05D40
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2005.09003
- Document Type :
- Working Paper