Lecture 8: Counting Binary Trees
This lecture provides a proof for the formula for the number of binary trees with n nodes.
It introduces the important concept of generating functions
Background Material
- Recursion and recurrence relations.
- binomial theorem and binomial coefficients.
- power series.
Reading
Review the material on generating combinatorial objects in
- Lecture 7 Recursive data structures and algorithm exploration.
Also study Maple's series command.
Topics
- Recurrence relation for the number of binary trees.
- Binomial theorem.
- Generating function for the number of binary trees.
- Functional equation
- Expanding using the binomial theorem.
- Asymptotics using Stirling's formula
Lecture Notes
- bintree.pdf - Notes on counting binary trees including review
of the binomial theorem, Stirling's formula, and a derivation of the formula and asymptotics
for the number of binary trees.
Assignments
Created: Oct. 26, 2006 by jjohnson@cs.drexel.edu