Aichholzer, O, Andritsch, L, Baur, K orcid.org/0000-0002-7665-476X et al. (1 more author) (2018) Perfect k-Colored Matchings and (k+2)-Gonal Tilings. Graphs and Combinatorics, 34 (6). pp. 1333-1346. ISSN 0911-0119
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © The Author(s) 2018. This is an open access article under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/) |
Keywords: | Triangulations; Perfect matchings; Temperley–Lieb algebras; Fuss–Catalan algebras |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Jan 2022 15:54 |
Last Modified: | 25 Jun 2023 22:51 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00373-018-1967-8 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:181777 |
Download
Filename: Aichholzer2018_Article_PerfectK-ColoredMatchingsAndK2.pdf
Licence: CC-BY 4.0