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This paper's aim is to present recent combinatorial considerations on r-Dyckpaths, r-Parking functions, and the r-Tamari lattices. Giving a betterunderstanding of the combinatorics of these objects has become important inview of their (conjectural) role in the description of the graded character ofthe Sn-modules of bivariate and trivariate diagonal coinvariant spaces for thesymmetric group.

Combinatorics of r-Dyck paths, r-Parking functions, and the r-Tamari lattices