Moments of Dyck paths
type: Item
instance of: scholarly article
title: Moments of Dyck paths
zbMATH Open document ID: 0932.05004
DOI: 10.1016/S0012-365X(98)00367-7
published in: Discrete Mathematics
publication date: 2000-03-13T00:00:00Z
review text: Dyck paths of semilength \(n\) are paths from \((0,0)\) to \((2n, 0)\) with steps (1, 1) and \((1,-1)\) which lie on or above the \(x\)-axis. Strict Dyck paths have only their endpoints on the \(x\)-axis. The area under a Dyck path is the area between the Dyck path and the \(x\)-axis. \textit{D. Merlini}, \textit{R. Sprugnoli}, and \textit{M. C. Verri} [Lect. Notes Comput. Sci. 1059, 59-71 (1996)] determined the average area under Dyck paths of semilength \(n\), and \textit{L. W. Shapiro}, \textit{W.-J. Woan}, and \textit{S. Getu} [SIAM J. Algebraic Discrete Methods 4, 459-466 (1983; Zbl 0524.05006)] determined the average area under strict Dyck paths of semilength \(n\). The present paper gives a way, using generating functions, to compute higher moments of these distributions.
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 1331467
zbMATH Keywords: Dyck paths
zbMATH Keywords: generating functions
zbMATH Keywords: moments
zbMATH Keywords: distributions
Wikidata QID: Q57942657
author: Robin Chapman
reviewed by: László A. Székely
MaRDI profile type: Publication
cites work: Dyck path enumeration
cites work: Q3669422
cites work: The area determined by underdiagonal lattice paths
cites work: The Catalan Numbers, the Lebesgue Integral, and 4 n-2
cites work: Runs, Slides and Moments
DBLP publication ID: journals/dm/Chapman99
description: scientific article; zbMATH DE number 1331467