Vol. 37, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Weighted lattice paths

Robert Dutton Fray and David Paul Roselle

Vol. 37 (1971), No. 1, 85–96
Abstract

A lattice path in the plane from (0,0) to (m,n) with weighted horizontal, vertical, and diagonal steps will be called a weighted lattice path. We determine the number of unrestricted weighted lattice paths, the number of paths below a line, and the number of paths which must remain between two parallel lines wilh unil slope. We also obtain generating functions for the number of paths which remain below the line y = x; these extend results obtained by Carlitz and Riordan for the ballot numbers.

Mathematical Subject Classification 2000
Primary: 05A15
Milestones
Received: 23 July 1970
Published: 1 April 1971
Authors
Robert Dutton Fray
David Paul Roselle