Lecture 12: Bivariate Generating Functions

A bivariate generating (BGF) is a formal power series in two variables. BGFs can be used to analyze the behaviour of a parameter of a family of combinatorial structures. For example, important parameters for binary trees are: height, number of leaves, path length. These parameters are important for algorithm analysis as they correspond to the performance of algorithms that compute with or are modeled by binary trees. One variable in the BGF is used to track the size of the structure (e.g. number of nodes in a binary tree) and the other is used to track the parameter of interest (e.g. height, number of leaves, path length).

Operations on BGFs can be used to compute the average value for a given parameter in all structures of a given size.

Background Material

Reading

Make sure you carefully study the Maple worksheet for this lecture. Additional handwritten notes are provided.

Topics

Maple worksheets and programs

Lecture Notes

Assignment

Created: Dec. 1, 2006 by jjohnson@cs.drexel.edu