Combinatorics of intervals in the plane I: trapezoids

05/18/2020

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by   Daniel Di Benedetto, et al.

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We study arrangements of intervals in 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.