English

A Note on Generalized Narayana Numbers

Combinatorics 2022-05-18 v1

Abstract

We give a simple proof that the the number of Dyck paths of semilength nn with ii returns to ground level and jj peaks is the generalized Narayana number in(nj)(ni1ji)\frac{i}{n} \binom{n}{j} \binom{n - i - 1}{j - i}.

Keywords

Cite

@article{arxiv.2205.08277,
  title  = {A Note on Generalized Narayana Numbers},
  author = {David Callan},
  journal= {arXiv preprint arXiv:2205.08277},
  year   = {2022}
}

Comments

4 pages

R2 v1 2026-06-24T11:19:45.528Z