Result: Moments, Narayana numbers, and the cut and paste for lattice paths
Title:
Moments, Narayana numbers, and the cut and paste for lattice paths
Authors:
Source:
Special issue on lattice path combinatorics and discrete distributions (in memory of I. Vincze)Journal of statistical planning and inference. 135(1):229-244
Publisher Information:
Amsterdam; Lausanne; New York,NY: Elsevier Science, 2005.
Publication Year:
2005
Physical Description:
print, 15 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Problèmes combinatoires classiques, Classical combinatorial problems, Probabilités et statistiques, Probability and statistics, Statistiques, Statistics, Lois de probabilités, Distribution theory, Décision statistique, Statistical decision, Decisión estadística, Fonction répartition, Distribution function, Función distribución, Moment statistique, Statistical moment, Momento estadístico, Méthode statistique, Statistical method, Método estadístico, Nombre Catalan, Catalan number, Número Catalan, Chemin lattice, Loi Narayana, Narayana distribution, Nombre Schroder, 05A15 Lattice path moments, Catalan numbers, Schröder numbers
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, Boise State University, Boise, ID, United States
ISSN:
0378-3758
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.17042305
Database:
PASCAL Archive
Further Information
Let U(n) denote the set of unrestricted lattice paths that run from (0, 0) to (n, 0) with permitted steps (1, 1), (1, - 1), and perhaps a horizontal step. Let E(n + 2) denote the set of paths in U(n + 2) that run strictly above the horizontal axis except initially and finally. First we review the cut-and-paste bisection which relates points under paths of E(n + 2) to points on paths of U(n). We apply it to obtain area and enumeration results for paths, some involving the Narayana distribution. We extend the cut-and-paste bijection to a formula relating factorial moments for the paths of E(n + 2) to factorial moments for the paths of U(n).