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

2012/02/28 by François Bergeron, Francois Bergeron, Bergeron, Francois · 1 citation
Computer Science · Mathematics · #05E05 #05E10 #05E18 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CO #msc:05E05 #msc:05E10 #msc:05E18

paper · pdf · doi:10.48550/arxiv.1202.6269

36 pages, 12 figures

openalex publication_date 2012/02/28 · arxiv created 2012/03/03 · arxiv updated 2012/03/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Higher Trivariate Diagonal Harmonics via generalized Tamari Posets

Cited by

• A simplicial complex spliting associativity

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