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Math 184 (Enumerative Combinatorics)

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Author(s): Steven V. Sam
Edition: version 2019-12-09
Year: 2019

Language: English
Commentary: Downloaded from https://math.ucsd.edu/~ssam/old/19F-184/notes.pdf

1. Review and introduction
1.1. Bijections
1.2. Sum and product principle
1.3. 12-fold way, introduction
1.4. Weak induction
1.5. Strong induction
2. Elementary counting problems
2.1. Permutations and combinations
2.2. Words
2.3. Choice problems
3. Partitions and compositions
3.1. Compositions
3.2. Set partitions
3.3. Integer partitions
3.4. 12-fold way, summary
4. Binomial theorem and generalizations
4.1. Binomial theorem
4.2. Multinomial theorem
4.3. Re-indexing sums
5. Formal power series
5.1. Definitions
5.2. Binomial theorem (general form)
6. Ordinary generating functions
6.1. Linear recurrence relations
6.2. Combinatorial interpretations
6.3. Catalan numbers
6.4. Composition of ordinary generating functions
7. Exponential generating functions
7.1. Definitions
7.2. Products of exponential generating functions
7.3. Compositions of exponential generating functions
7.4. Lagrange inversion formula
8. Sieving methods
8.1. Inclusion-exclusion
8.2. Möbius inversion