### 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 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.

Original language | English |
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Title of host publication | Proc. $33^rd$ European Workshop on Computational Geometry EuroCG '17 |

Place of Publication | Malmö, Sweden |

Pages | 81-84 |

Number of pages | 4 |

Publication status | Published - 2017 |

## Cite this

Aichholzer, O., Andritsch, L., Baur, K., & Vogtenhuber, B. (2017). Perfect $k$-colored matchings and $k+2$-gonal tilings. In

*Proc. $33^rd$ European Workshop on Computational Geometry EuroCG '17*(pp. 81-84). Malmö, Sweden.