Parametric Production Matrices and
Weighted Succession Rules: a Dyck Path
ARC Centre of Excellence for Mathematics
and Statistics of Complex Systems
The University of Melbourne
139 Barry Street
We introduce weighted succession rules and parametric production
matrices --- simple extensions of the standard ECO method succession
rules and production matrices. The purpose is to enumerate
combinatorial objects with respect to several variables. We consider
one main example, from the theory of Dyck paths. The path statistics
primarily considered are peak height, rise height, and certain
subwalks. Many classical sequences (such as the Catalan, Motzkin,
Narayana and Schroeder numbers) are incorporated in this example.
Full version: pdf,
(Concerned with sequences
Received January 29 2007;
revised version received June 6 2007.
Published in Journal of Integer Sequences, June 6 2007.
Journal of Integer Sequences home page