2025/01/23 by Helmut Prodinger, Prodinger, Helmut
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2501.13645
openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motzkin paths consist of up-steps, down-steps, horizontal steps, never go below the x-axis and return to the x-axis. Versions where the return to the x-axis isn't required are also considered. A path is peakless (valleyless) if UD (if DU) never occurs. If it is both peakless and valleyless, it is called cornerless. Deutsch and Elizalde have linked cornerless Motzkin paths and bargraphs bijectly. Thus, instead of prefixes of bargraphs one might consider prefixes of cornerless Motzkin paths. In this paper, this is extended by counting the occurrences of UD resp., DU. The concepts are extended to so-called skew Motzkin paths. Methods are generating functions and the kernel method to compute explicit forms.