Part IX · Number Theory, Combinatorics and Algebra
54. Combinatorics, Counting and Enumeration
8 lessons•34 topics•Intermediate / Expert
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54.01Outline
Basic counting
- Permutations
- Combinations
- Variations with repetition
- Multisets
- Product rule
- Sum rule
54.02Outline
Binomial identities
- Pascal triangle
- Binomial theorem
- Hockey-stick identity
- Stars and bars
54.03Outline
Inclusion-exclusion
- Count avoiding forbidden properties
- Derangements
- Surjections
- Multiples union
54.04Outline
Catalan family
- Balanced parentheses
- BST shapes
- Polygon triangulations
- Dyck paths
54.05Outline
Stirling and Bell numbers
- Stirling first kind
- Stirling second kind
- Bell numbers
- Set partitions
54.06Outline
Pigeonhole and invariants
- Pigeonhole principle
- Extremal principle
- Parity invariant
- Coloring invariant
54.07Outline
Generating functions
- Ordinary generating functions
- Exponential generating functions
- Coefficient extraction introduction
54.08Outline
Burnside and Polya
- Group actions
- Orbits
- Burnside's lemma
- Rotational colorings
- Polya enumeration overview