Staircase tilings and \(k\)-Catalan structures

DOI10.1016/j.disc.2007.11.012zbMath1158.05006OpenAlexW2020459909MaRDI QIDQ998328

Silvia Heubach, Toufik Mansour, Nelson Y. Li

Publication date: 28 January 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.11.012

zbMATH Keywords

\(k\)-ary tree\(k\)-ary number\(k\)-Catalan numberset-valued Young tableaustaircase tiling

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of representation theory (05E10) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (27)

A family of Bell transformations ⋮ Colored Motzkin Paths of Higher Order ⋮ Raney numbers, threshold sequences and Motzkin-like paths ⋮ On the enumeration of non-crossing pairings of well-balanced binary strings ⋮ Generalized Path Pairs and Fuss-Catalan Triangles ⋮ Modular Fuss-Catalan numbers ⋮ Protected points in \(k\)-ary trees ⋮ Enumeration of generalized Dyck paths based on the height of down-steps modulo \(k\) ⋮ Refined enumeration of \(k\)-plane trees and \(k\)-noncrossing trees ⋮ Unnamed Item ⋮ The \(m\)-Schröder paths and \(m\)-Schröder numbers ⋮ Unnamed Item ⋮ Counting humps and peaks in generalized Motzkin paths ⋮ Unnamed Item ⋮ Critical behavior of colored tensor models in the large \(N\) limit ⋮ Factorizations related to the reciprocal Pascal matrix ⋮ Lattice paths and generalized cluster complexes ⋮ Unnamed Item ⋮ Bijections on \(r\)-Shi and \(r\)-Catalan arrangements ⋮ Enumerations of rational non-decreasing Dyck paths with integer slope ⋮ Set-Valued Tableaux & Generalized Catalan Numbers ⋮ Set-Valued Young Tableaux and Product-Coproduct Prographs ⋮ Efficient generation, ranking, and unranking of \((k,m)\)-ary trees in B-order ⋮ The dual of number sequences, Riordan polynomials, and Sheffer polynomials ⋮ Some properties of the Fuss-Catalan numbers ⋮ Unnamed Item ⋮ Enumerations of humps and peaks in \((k, a)\)-paths and \((n, m)\)-Dyck paths via bijective proofs

Uses Software

• OEIS

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