Asymptotic results for the number of paths in a grid

Simple item page
dc.contributor.authorPanholzer A.
dc.contributor.authorProdinger H.
dc.date.accessioned2012-06-06T07:59:00Z
dc.date.available2012-06-06T07:59:00Z
dc.date.issued2012
dc.description.abstractIn two recent papers, Albrecht and White ['Counting paths in a grid', Austral. Math. Soc. Gaz. 35 (2008), 43-48] and Hirschhorn ['Comment on "Counting paths in a grid", Austral. Math. Soc. Gaz. 36 (2009), 50-52] considered the problem of counting the total number Pm,n of certain restricted lattice paths in an m × n grid of cells, which appeared in the context of counting train paths through a rail network. Here we give a precise study of the asymptotic behaviour of these numbers for the square grid, extending the results of Hirschhorn, and furthermore provide an asymptotic equivalent of these numbers for a rectangular grid with a constant proportion α = m/n between the side lengths. © 2011 Australian Mathematical Publishing Association Inc.
dc.identifier.citationBulletin of the Australian Mathematical Society
dc.identifier.citation85
dc.identifier.citation3
dc.identifier.citation446
dc.identifier.citation455
dc.identifier.issn49727
dc.identifier.otherdoi:10.1017/S0004972711002759
dc.identifier.urihttp://hdl.handle.net/10019.1/21247
dc.subjectAsymptotic enumeration
dc.subjectDiagonalization method
dc.subjectRestricted lattice paths
dc.subjectSaddle point method
dc.titleAsymptotic results for the number of paths in a grid
dc.typeArticle
Files
Collections
Stellenbosch University - Scopus Publications