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

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

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.
Originalspracheenglisch
TitelProc. $33^rd$ European Workshop on Computational Geometry EuroCG '17
ErscheinungsortMalmö, Sweden
Seiten81-84
Seitenumfang4
PublikationsstatusVeröffentlicht - 2017

Dieses zitieren

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 (S. 81-84). Malmö, Sweden.