Partial difference equation method for lattice path problems
type: Item
instance of: scholarly article
title: Partial difference equation method for lattice path problems
zbMATH Open document ID: 0934.05004
DOI: 10.1007/BF01608787
author: J. W. Essam
author: R. Brak
author: Aleksander L. Owczarek
published in: Annals of Combinatorics
publication date: 2000-04-10T00:00:00Z
review text: The authors recently have exactly solved the problems of the enumeration of paths on a square lattice [J. Stat. Phys. 93, No. 1-2, 155-192 (1998)], evaluating the partition functions. In this paper they discuss the application of the partial difference equation method for the case of one path in a half-plane, comparing it with the transfer matrix method, and show that this method can be easily generalized to many intersecting paths.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 82B41
zbMATH DE Number: 1347712
zbMATH Keywords: random walks
zbMATH Keywords: lattice paths
zbMATH Keywords: partition
zbMATH Keywords: partial difference equation
zbMATH Keywords: transfer matrix method
zbMATH Keywords: intersecting paths
MaRDI profile type: Publication
cites work: Exact solution ofNdirected non-intersecting walks interacting with one or two boundaries
cites work: From the Bethe Ansatz to the Gessel-Viennot theorem
cites work: New results for directed vesicles and chains near an attractive wall
cites work: Walks, walls, wetting, and melting
cites work: Binomial determinants, paths, and hook length formulae
cites work: Vicious walkers and Young tableaux I: without walls
description: scientific article; zbMATH DE number 1347712