The 136th manifestation of C_n

2005/11/01 by David Callan, Callan, David
Mathematics · #05A15 #05A19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #math.CO #msc:05A15 #msc:05A19

paper · pdf · doi:10.48550/arxiv.math/0511010

3 pages, LaTeX

arxiv created 2005/11/01 · openalex publication_date 2005/11/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show bijectively that the Catalan number C_n counts Dyck (n+1)-paths in which the terminal descent is of even length and all other descents to ground level (if any) are of odd length.

Related

• Counting generalized Dyck paths
• Bijections for Dyck paths with all peak heights of the same parity
• Prefixes of Stanley's Catalan paths with odd returns to the x-axis -- standard version and skew Catalan-Stanley paths
• Knight's paths towards Catalan numbers
• Raised k-Dyck paths