%A Fusy, Éric
%A Humbert, Abel
%D 2019
%T Bijections for generalized Tamari intervals via orientations
%K
%X 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.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1297
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 701-708%V 88
%N 3
%@ 0862-9544
%8 2019-07-30