2020/06/02 by Shalosh B. Ekhad, Doron Zeilberger, Ekhad, Shalosh B. +1 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Database Systems and Queries #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2006.01961
openalex publication_date 2020/06/02 · openalex created_date 2020/06/12 · openalex updated_date 2026/07/28
Dyck paths are one of the most important objects in enumerative combinatorics, and there are many papers devoted to counting selected families of Dyck paths. Here we present two approaches for the automatic counting of many such families, using both a "dumb" approach (driven by numeric dynamic programming) that often works in practice, and a "clever" approach, needed for larger problems, driven by "symbolic" dynamic programming. Both approaches are fully automated and implemented in Maple.