List of combinatorics topics

This is a list of combinatorics topics, by Wikipedia page.

A few decades ago it might have been said that combinatorics is to mathematics roughly what irritable bowel syndrome is to gastroenterology - a way to classify poorly-understood problems, and some standard remedies. Great progress has been made since 1960.

This page is complementary to the list of graph theory topics: graph theory being the part of combinatorial mathematics that is most like a separate discipline. In general, combinatorics is as much about problem solving as theory building.

Since combinatorial mathematics is effectively the environment for the study of data structures in computer science, there are very many topics that arise there. The same could be said for other fields, such as error-correcting codes, bioinformatics.

Table of contents

1 General combinatorial principles and methods
2 Problem solving as an art
3 Some general theories
4 Topics
5 Letters
6 Data structure concepts
7 People

General combinatorial principles and methods

To begin with, some general principles:

Trial and error, brute force search, bogosort
Pigeonhole principle
Mathematical induction
Recurrence relation
Generating functions as an application of formal power series
Binomial coefficients and their properties
Double counting
Inclusion-exclusion principle
M�bius inversion formula
Even permutations
Incidence algebra
Greedy algorithm
Divide and conquer
- Akra-Bazzi Method
Dynamic programming
Birthday attack, birthday paradox
Reduction to linear algebra
Umbral calculus
Minimax algorithm
- Alpha-beta pruning
Probabilistic method
sieve method