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3: Generating Functions

Last updated

Oct 1, 2023
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- 2.E: Inclusion-Exclusion (Exercises)
- 3.1: Prelude to Generating Functions

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3.1: Prelude to Generating Functions
3.2: Newton's Binomial Theorem
3.3: Exponential Generating Functions
3.4: Partitions of Integers
3.5: Recurrence Relations
A recurrence relation defines a sequence by expressing a typical term in terms of earlier terms. Note that some initial values must be specified for the recurrence relation to define a unique sequence. The starting index for the sequence need not be zero if it doesn't make sense or some other starting index is more convenient.
3.6: Catalan Numbers
A rooted binary tree is a type of graph that is particularly of interest in some areas of computer science. The root is the topmost vertex. The vertices below a vertex and connected to it by an edge are the children of the vertex. It is a binary tree because all vertices have 0, 1, or 2 children. How many different rooted binary trees are there with n vertices? Let us denote this number by Cn; these are the Catalan numbers.
3.E: Generating Functions (Exercises)

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