A bijective approach to the area of generalized Motzkin paths

DOI10.1006/aama.2001.0796zbMath1005.05008OpenAlexW1981226844WikidataQ114234245 ScholiaQ114234245MaRDI QIDQ696823

Robert A. Sulanke, Simone Rinaldi, Renzo Pinzani, Elisa Pergola

Publication date: 12 September 2002

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.2001.0796

zbMATH Keywords

recurrencelattice paths

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15)

Related Items

Area-width scaling in generalised Motzkin paths ⋮ The height of two types of generalised Motzkin paths ⋮ Lattice path moments by cut and paste ⋮ Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences ⋮ Algorithms for counting minimum-perimeter lattice animals ⋮ Non-uniform random generation of generalized Motzkin paths ⋮ On Two Subclasses of Motzkin Paths and Their Relation to Ternary Trees ⋮ On Computing the Total Displacement Number via Weighted Motzkin Paths ⋮ Limits of areas under lattice paths ⋮ Random walks in octants, and related structures ⋮ Motzkin paths, Motzkin polynomials and recurrence relations

Cites Work

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• Some \(q\)-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths
• Bijective recurrences concerning Schröder paths
• A combinatorial interpretation of the recurrence \(f_{n+1}=6f_n-f_{n-1}\)
• A combinatorial interpretation of the area of Schröder paths
• The Catalan Numbers, the Lebesgue Integral, and 4 n-2
• Two bijections for the area of Dyck paths
• Bijective recurrences for Motzkin paths