Counting generalized Dyck paths
Combinatorics
2013-04-23 v1
Abstract
The Catalan number has a lot of interpretations and one of them is the number of Dyck paths. A Dyck path is a lattice path from to which is below the diagonal line . One way to generalize the definition of Dyck path is to change the end point of Dyck path, i.e. we define (generalized) Dyck path to be a lattice path from to which is below the diagonal line , and denote by the number of Dyck paths from to . In this paper, we give a formula to calculate for arbitrary and .
Keywords
Cite
@article{arxiv.1304.5595,
title = {Counting generalized Dyck paths},
author = {Yukiko Fukukawa},
journal= {arXiv preprint arXiv:1304.5595},
year = {2013}
}
Comments
15 pages, 2 figures