English

An identity for the central binomial coefficient

Combinatorics 2012-06-15 v1

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.

Keywords

Cite

@article{arxiv.1206.3174,
  title  = {An identity for the central binomial coefficient},
  author = {David Callan},
  journal= {arXiv preprint arXiv:1206.3174},
  year   = {2012}
}

Comments

5 pages

R2 v1 2026-06-21T21:19:24.091Z