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

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.

arXiv comment36 pages, 12 figures

References in corpus (5)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Higher Trivariate Diagonal Harmonics via generalized Tamari Posets
• Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups
• Tamari lattices and parking functions: proof of a conjecture of F. Bergeron
• The Topology of the $m$-Tamari Lattices

Cited by in corpus (5)

• Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions
• m-dendriform algebras
• Some aspects of (r,k)-parking functions
• Maximal degree subposets of $\nu$-Tamari lattices
• A simplicial complex spliting associativity