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
- Recursion and recurrence relations.
- binomial theorem and binomial coefficients.
- power series.
Review the material on generating combinatorial objects in
Also study Maple's series command.
- Lecture 7 Recursive data structures and algorithm exploration.
- 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
- 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.
Created: Oct. 26, 2006 by email@example.com