Automatic Counting of Restricted Dyck Paths via (Numeric and Symbolic) Dynamic Programming
arXiv:2006.01961
Abstract
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.
13 pages. Accompanied by two Maple packages available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/dyck.html .Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and this arxiv. This version has a few references to previous work added