Author(s): Steven V. Sam
Edition: version 2018-12-03
Year: 2018
Language: English
Commentary: Downloaded from https://math.ucsd.edu/~ssam/old/18F-184A/notes.pdf
1. Pigeon-hole principle
1.1. Basic version
1.2. General version
2. Induction
2.1. Weak induction
2.2. Strong induction
3. Elementary counting problems
3.1. Functions
3.2. 12-fold way, introduction
3.3. Permutations and combinations
3.4. Words
3.5. Choice problems
4. Partitions and compositions
4.1. Compositions
4.2. Set partitions
4.3. Integer partitions
4.4. 12-fold way, summary
5. Binomial theorem and generalizations
5.1. Binomial theorem
5.2. Multinomial theorem
6. Inclusion-exclusion
7. Formal power series
7.1. Definitions
7.2. Binomial theorem (general form)
8. Ordinary generating functions
8.1. Linear recurrence relations
8.2. Combinatorial interpretations
8.3. Catalan numbers
8.4. Composition of ordinary generating functions
9. Exponential generating functions
9.1. Definitions
9.2. Products of exponential generating functions
9.3. Compositions of exponential generating functions
9.4. Lagrange inversion formula
10. Partially ordered sets
10.1. Definitions and examples
10.2. The incidence algebra
10.3. Möbius inversion
