Arcs on spheres intersecting at most twice

Christopher Smith; Piotr Przytycki

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arXiv · 1707.07818

Arcs on spheres intersecting at most twice

Christopher Smith·Piotr Przytycki

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Abstract

Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set of arcs pairwise intersecting at most once, which start at p and end in Q, is |X|(|X| + 1). We deduce that the maximal cardinality of a set of arcs with arbitrary endpoints pairwise intersecting at most twice is |X|(|X| + 1)(|X| + 2).

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Christopher Smith, Piotr Przytycki. 2017-07-25. Arcs on spheres intersecting at most twice. https://arxiv.org/abs/1707.07818

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