2004/07/22 by David Callan, Callan, David
Computer Science · Mathematics · #05A15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #Topological and Geometric Data Analysis #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0407374
8 pages,LaTeX
arxiv created 2004/07/22 · openalex publication_date 2004/07/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give several bijections among restricted Motzkin paths, explaining why various parameters on these paths are equidistributed. For example, the number of doublerise-free Motzkin paths of length n is the same as the number of peak-free Motzkin paths of length n+1 and the parameter "number of doublefalls" has the same distribution on the former set as "number of valleys" does on the latter. The bijections are most easily presented recursively but we also give explicit descriptions using the notion of Motzkin tree.