An identity for the central binomial coefficient

2012/06/14 by David Callan, Callan, David
Mathematics · #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.1206.3174

5 pages

arxiv created 2012/06/14 · openalex publication_date 2012/06/14 · arxiv updated 2012/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find the joint distribution of three simple statistics on lattice paths of n upsteps and n downsteps leading to a triple sum identity for the central binomial coefficient 2n-choose-n. We explain why one of the constituent double sums counts the irreducible pairs of compositions considered by Bender et al., and we evaluate some of the other sums.

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