On pairs of lattice paths with a given number of intersections
type: Item
instance of: scholarly article
title: On pairs of lattice paths with a given number of intersections
zbMATH Open document ID: 0874.05004
author: Markus Fulmek
published in: Journal of Combinatorial Theory. Series A
publication date: 1997-11-09T00:00:00Z
review text: The author gives another proof for the number of ordered pairs of paths in the integer lattice \(\mathbb{Z}\times\mathbb{Z}\) with a prescribed number of intersection points. This is done by constructing a bijection algorithm between the set of these pairs and some combinatorial set generated by nonintersecting pairs. The first formula for the mentioned number was recently given by \textit{I. M. Gessel} and \textit{W. Shur} [J. Comb. Theory, Ser. A 75, No. 2, 243-253, Art. No. 0075 (1996; Zbl 0866.05002)]. In conclusion some complicated binomial identities are established.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1016778
zbMATH Keywords: lattice paths
zbMATH Keywords: intersection number
zbMATH Keywords: number of ordered pairs of paths
zbMATH Keywords: integer lattice
zbMATH Keywords: binomial identities
MaRDI profile type: Publication
OpenAlex ID: W2034051839
cites work: Counting pairs of lattice paths by intersections
cites work: Even and odd pairs of lattice paths with multiple intersections
cites work: Nonintersecting paths, pfaffians, and plane partitions
DOI: 10.1006/JCTA.1996.2754
description: scientific article; zbMATH DE number 1016778