Result: Moments, Narayana numbers, and the cut and paste for lattice paths

Title:
Moments, Narayana numbers, and the cut and paste for lattice paths
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
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
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).