Journal of Integer Sequences, Vol. 10 (2007), Article 07.6.1

Parametric Production Matrices and Weighted Succession Rules: a Dyck Path Example

Robert Parviainen
ARC Centre of Excellence for Mathematics and Statistics of Complex Systems
The University of Melbourne
139 Barry Street
3010 Victoria


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.

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(Concerned with sequences A000045 A000108 A001003 A001006 A001263 A001700 A002212 A007318 A011973 A039598 A091869 A098979 A114687 A126181 A126182 and A126216 .)

Received January 29 2007; revised version received June 6 2007. Published in Journal of Integer Sequences, June 6 2007.

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