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.
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