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Notes for Math 184A (Combinatorics)

✍ Scribed by Steven V. Sam


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

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✦ 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. MΓΆbius inversion

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MATH 155R Algebriac Combinatorics Lectur
✍ Lauren Williams, Alec Sun πŸ“‚ Library πŸ“… 2019 🌐 English

This undergraduate course on Algebraic Combinatorics is taught by Professor Lauren Williams. The webpage is at http://www.math.harvard.edu/~williams/155.html.