School Seminars and Colloquia

The ECO method with many parameters

Statistical Mechanics/Combinatorics Seminar

by Robert Parviainen

Institution: The University of Melbourne
Date: Thu 9th August 2007
Time: 3:15 PM
Location: Room 213, Dept. of Mathematics & Statistics, Uni of Mel

Abstract: The Enumerating Combinatorial Objects (ECO) method is a framework for enumerating
objects with a recursive structure. It has been most successful in the patterns in permutations
area, but also gives nice result for some lattice path and polygon problems.

After recalling the basics, I will describe a simple extension of the standard ECO method.
The aim of this (as yet unnamed) extension is to allow for enumeration with respect to many
(as in possibly infinitely many) parameters.

I will show a lattice path application, where we enumerate paths with respect to infinitely
many parameters: the number of peaks of each height, which also is shown by the method to be
equivalent to heights of rises. The Catalan, Motzkin, Pascal, Narayana and Schröder
numbers triangles are just some of the special cases included in this example.

For More Information: Dr Iwan Jensen