Counting lattice paths in restricted planes
type: Item
instance of: scholarly article
title: Counting lattice paths in restricted planes
zbMATH Open document ID: 0943.05006
DOI: 10.1016/S0012-365X(99)00287-3
author: Seul Hee Choi
published in: Discrete Mathematics
publication date: 2000-03-22T00:00:00Z
review text: The author proves a complicated formula for the number of lattice paths of fixed length on a square lattice, contained in the plane sector \(0\leq y\leq x\), as well as for paths of this kind that do not cross the line \(y=-x+ a\) \((a>0)\). In the proofs the techniques of enumeration of noncrossing paths [see \textit{I. M. Gessel} and \textit{X. Viennot}, Adv. Math. 58, 300-321 (1985; Zbl 0579.05004)] and of Young tableaux [compare \textit{D. Gouyou-Beauchamps}, Eur. J. Comb. 10, No. 1, 69-82 (1989; Zbl 0672.05012)] are used. Some expressions involve Catalan numbers.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 1421656
zbMATH Keywords: lattice paths
zbMATH Keywords: enumeration
zbMATH Keywords: noncrossing paths
zbMATH Keywords: Young tableaux
zbMATH Keywords: Catalan numbers
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00287-3
OpenAlex ID: W2038465232
description: scientific article; zbMATH DE number 1421656