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

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

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 languageEnglish
Title of host publicationProc. $33^rd$ European Workshop on Computational Geometry EuroCG '17
Place of PublicationMalmö, Sweden
Pages81-84
Number of pages4
Publication statusPublished - 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.

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

Proc. $33^rd$ European Workshop on Computational Geometry EuroCG '17. Malmö, Sweden, 2017. p. 81-84.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

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. Malmö, Sweden, pp. 81-84.
Aichholzer O, Andritsch L, Baur K, Vogtenhuber B. Perfect $k$-colored matchings and $k+2$-gonal tilings. In Proc. $33^rd$ European Workshop on Computational Geometry EuroCG '17. Malmö, Sweden. 2017. p. 81-84
Aichholzer, O. ; Andritsch, L. ; Baur, K. ; Vogtenhuber, B. / Perfect $k$-colored matchings and $k+2$-gonal tilings. Proc. $33^rd$ European Workshop on Computational Geometry EuroCG '17. Malmö, Sweden, 2017. pp. 81-84
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