Abstract
The crossing lemma holds in because a real line separates the plane into two disjoint regions. In removing a complex line keeps the remaining point-set connected. We investigate the crossing structure of affine line segment-like objects in by defining two notions of line segments between two points and give computational results on combinatorics of crossings of line segments induced by a set of points. One way we define the line segments motivates a related problem in , which we introduce and solve.
Citation
Samuli Leppänen. "Crossings of complex line segments." Involve 8 (2) 285 - 294, 2015. https://doi.org/10.2140/involve.2015.8.285
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