2023/08/06 by Helmut Prodinger, Prodinger, Helmut
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2308.03080
openalex publication_date 2023/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There was recent interest in Motzkin paths without peaks (peak: up-step followed immediately by down-step); additional results about this interesting family is worked out. The new results are the enumeration of such paths that live in a strip [0..ℓ], and as consequence the asymptotics of the average height, which is given by 2⋅ 5-1/4√(πn). Methods include the kernel method and singularity analysis of generating functions.