2021/11/25 by Gennady Eremin, Eremin, Gennady
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2111.13060
openalex publication_date 2021/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dyck paths are among the most heavily studied Catalan families. We work with peaks and valleys to uniquely decompose Dyck paths into the simplest objects - prime fragments with a single peak. Each Dyck path is uniquely characterized by a set of peaks or a set of valleys. The appendix contains a python program with which the reader can factorize Dyck paths online.