Lecture 9: Generating Functions
This lecture continues the theme of using Maple to investigate the performance
of algorithms and generating combinatorial objects. The lecture introduces
generating functions which are a very important tool for analyzing integer
sequences, recurrence relations, and combinatorial objects.
- Recursion and recurrence relations.
- Power series.
- Taylor series.
Review the material on generating combinatorial objects in
Also study Maple's series command.
- Introduction to generating functions (simple examples and elementary properties)
- Fibonacci numbers
- Harmonic numbers
- Number of binary trees
- Number of partition trees
- Functional equations
- from recurrence relations (eg. Hanoi, Fibonacci, convolution and
- from combinatorial constructions (binary trees, partition trees)
- Solving recurrence relations using generating functions
- partial fractions (Hanoi, Fibonacci)
- binomial theorem (number of binary trees)
Maple worksheets and programs and other resources
- gen.mw - Maple worksheet on generating functions.
Created: Oct. 26, 2006 by email@example.com