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arXiv · 1710.06757

Perfect k-colored matchings and (k+2)-gonal tilings

Oswin Aichholzer·Lukas Andritsch·Karin Baur·Birgit Vogtenhuber
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Abstract

We derive a simple bijection between geometric plane perfect matchings on $2n$ points in convex position and triangulations on $n+2$ points in convex position. We then extend this bijection to monochromatic plane perfect matchings on periodically $k$-colored vertices and $(k+2)$-gonal tilings of convex point sets. These structures are related to a generalization of Temperley-Lieb algebras and our bijections provide explicit one-to-one relations between matchings and tilings. Moreover, for a given element of one class, the corresponding element of the other class can be computed in linear time.

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Oswin Aichholzer, Lukas Andritsch, Karin Baur, Birgit Vogtenhuber. 2017-10-18. Perfect k-colored matchings and (k+2)-gonal tilings. https://arxiv.org/abs/1710.06757

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