### Abstract

Original language | English |
---|---|

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

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

**Perfect $k$-colored matchings and $k+2$-gonal tilings.** / Aichholzer, O.; Andritsch, L.; Baur, K.; Vogtenhuber, B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

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

}

TY - GEN

T1 - Perfect $k$-colored matchings and $k+2$-gonal tilings

AU - Aichholzer, O.

AU - Andritsch, L.

AU - Baur, K.

AU - Vogtenhuber, B.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

M3 - Conference contribution

SP - 81

EP - 84

BT - Proc. $33^rd$ European Workshop on Computational Geometry EuroCG '17

CY - Malmö, Sweden

ER -