Notes for Math 184A (Combinatorics)

✍ Scribed by Steven V. Sam

• Year: 2018
• Tongue: English
• Leaves: 46
• Edition: version 2018-12-03
• Category: Library

✦ Table of Contents

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