Bijections for generalized Tamari intervals via orientations

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Éric Fusy Abel Humbert

Abstract

We introduce two bijections for generalized Tamari intervals, which were recently introduced by Préville-Ratelle and Viennot, and proved to be in bijection with rooted non-separable maps by Fang and Préville-Ratelle. Our first construction proceeds via separating decompositions on quadrangulations and can be seen as an extension of the Bernardi-Bonichon bijection between Tamari intervals and minimal Schnyder woods. Our second construction directly exploits the Bernardi-Bonichon bijection and  the point of view of generalized Tamari intervals as a special case of classical Tamari intervals (synchronized Tamari intervals); it yields a trivariate generating function expression that interpolates between generalized Tamari intervals and classical Tamari intervals.

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How to Cite
Fusy, ., & Humbert, A. (2019). Bijections for generalized Tamari intervals via orientations. Acta Mathematica Universitatis Comenianae, 88(3), 701-708. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1297/715
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EUROCOMB 2019