Explicit expression for the generating function counting Gessel's walks

Abstract : Gessel's walks are the planar walks that move within the positive quadrant $\mathbb{Z}_{+}^{2}$ by unit steps in any of the following directions: West, North-East, East and South-West. In this paper, we find an explicit expression for the trivariate generating function counting the Gessel's walks with $k\geq 0$ steps, which start at $(0,0)$ and end at a given point $(i,j) \in \mathbb{Z}^2_+$.
Document type :
Journal articles
Advances in Applied Mathematics, Elsevier, 2011, 47, pp.414-433
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00438190
Contributor : Kilian Raschel <>
Submitted on : Thursday, November 18, 2010 - 2:10:06 PM
Last modification on : Monday, May 29, 2017 - 2:22:57 PM
Document(s) archivé(s) le : Saturday, December 3, 2016 - 12:54:31 AM

Files

Gessel_IK_KR_final.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00438190, version 3

Collections

UPMC | PMA | INSMI | USPC

Citation

Irina Kurkova, Kilian Raschel. Explicit expression for the generating function counting Gessel's walks. Advances in Applied Mathematics, Elsevier, 2011, 47, pp.414-433. <hal-00438190v3>

Share

Metrics

Record views

229

Document downloads

49