Limits of areas under lattice paths

DOI10.1016/j.disc.2008.11.020zbMath1228.05032OpenAlexW2059881677MaRDI QIDQ1043560

Brian Drake

Publication date: 9 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.disc.2008.11.020

zbMATH Keywords

Motzkin pathsgeneralized Frobenius partitionsSchröder paths

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15)

Related Items (6)

Schröder partitions, Schröder tableaux and weak poset patterns ⋮ Restricted growth function patterns and statistics ⋮ Generalized Frobenius partitions, Motzkin paths, and Jacobi forms ⋮ Counting lattice paths with four types of steps ⋮ Some statistics on generalized Motzkin paths with vertical steps ⋮ Some combinatorial properties of hexagonal lattices

Uses Software

• OEIS

Cites Work

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• A bijective approach to the area of generalized Motzkin paths
• q-Catalan numbers
• Some \(q\)-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths
• Bijective recurrences concerning Schröder paths
• Algebraic languages and polyominoes enumeration
• A weight-preserving bijection between Schröder paths and Schröder permutations
• A combinatorial interpretation of the area of Schröder paths
• Two element lattice permutation numbers and their \(q\)-generalization
• Generalized Frobenius partitions
• A Noncommutative Generalization and q-Analog of the Lagrange Inversion Formula
• On Some Alternative Characterizations of Riordan Arrays
• Motzkin numbers of higher rank: Generating function and explicit expression
• The area determined by underdiagonal lattice paths
• An area-to-inv bijection between Dyck paths and 312-avoiding permutations

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