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.
Original language | English |
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Pages (from-to) | 1333-1346 |
Number of pages | 14 |
Journal | Graphs and Combinatorics |
Volume | 34 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2018 |