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Perfect k-Colored Matchings and (k+2)-Gonal Tilings
- Publication Year :
- 2018
- Publisher :
- Springer, 2018.
-
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.<br />Comment: 12 pages, 8 figures
- Subjects :
- FOS: Mathematics
Mathematics - Combinatorics
Combinatorics (math.CO)
Subjects
Details
- Language :
- English
- ISSN :
- 09110119
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....20d859cb8ceabe51847c11fda0f74b0b