Counting peaks at height k in a Dyck path
| dc.creator | Mansour, T. | |
| dc.date | 2002-03-21 | |
| dc.date | 2002-05-02 | |
| dc.date.accessioned | 2026-07-07T04:47:13Z | |
| dc.date.available | 2026-07-07T04:47:13Z | |
| dc.description | A Dyck path is a lattice path in the plane integer lattice $\mathbb{Z}\times\mathbb{Z}$ consisting of steps (1,1) and (1,-1), which never passes below the x-axis. A peak at height k on a Dyck path is a point on the path with coordinate y=k that is immediately preceded by a (1,1) step and immediately followed by a (1,-1) step. In this paper we find an explicit expression to the generating function for the number of Dyck paths starting at (0,0) and ending at (2n,0) with exactly r peaks at height k. This allows us to express this function via Chebyshev polynomials of the second kind and generating function for the Catalan numbers. | |
| dc.description | 7 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0203222 | |
| dc.identifier | http://arxiv.org/abs/math/0203222 | |
| dc.identifier | Journal of Integer Sequences 5, (2002), Article 02..1.1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63624 | |
| dc.subject | Combinatorics | |
| dc.title | Counting peaks at height k in a Dyck path | |
| dc.type | text |