Outline of combinatorics
This is a list of combinatorics topics, by Wikipedia page.
As combinatorics is to mathematics roughly what irritable bowel syndrome is to gastroenterology - a way to classify poorly-understood problems, and some standard remedies - some further explanations are required. This page is complementary to the list of graph theory topics: graph theory being one of the parts of combinatorial mathematics that is most like a separate discipline. In general, combinatorics is as much about problem solving as theory building.
To begin with, some general principles:
General combinatorial principles and methods
- Trial and error, brute force search, bogosort
- Pigeonhole principle
- Mathematical induction
- Recursion relation
- Generating functions as application of formal power series
- Binomial coefficients and their properties
- Double counting
- Inclusion-exclusion formula
- Möbius inversion formula
- Incidence algebra
- Greedy algorithm
- Divide and conquer
- Dynamic programming
- Reduction to linear algebra
- Umbral calculus
- Alpha-beta pruning
- Probabilistic method
Problem solving as an art
Some general theories
- Matroid
- Ramsey theory
- Binomial type polynomial sequences