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We derive a simple bijection between geometric plane perfect matchings on 2 n 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.

Perfect k-Colored Matchings and $$(k+2)$$ ( k + 2 ) -Gonal Tilings