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Automatic Counting of Restricted Dyck Paths via (Numeric and Symbolic) Dynamic Programming - MaRDI portal

Automatic Counting of Restricted Dyck Paths via (Numeric and Symbolic) Dynamic Programming

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Publication:6341972

arXiv2006.01961MaRDI QIDQ6341972

Doron Zeilberger, Shalosh B. Ekhad

Publication date: 2 June 2020

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.












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