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.
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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
- Möbius inversion formula
- Even permutations
- Incidence algebra
- Greedy algorithm
- Divide and conquer
- Dynamic programming
- Birthday attack, birthday paradox
- Reduction to linear algebra
- Umbral calculus
- Minimax algorithm
- Probabilistic method
- sieve method
Problem solving as an art
Some general theories
- Matroid
- Ramsey theory
- Binomial type polynomial sequences
- Combinatorial species
Topics
- Assignment problem
- Barcode
- Boolean satisfiability problem, satisfiability problem (duplication!)
- Catalan number
- Cellular automaton
- Collatz conjecture
- Combination
- Combinatorial search
- Data integrity
- Deadlock
- Derangement
- Dickson's lemma
- Eight queens puzzle
- Enumeration
- Erdös-Ko-Rado theorem
- Faà di Bruno's formula
- Fifteen puzzle
- Finite geometry
- Game theory
- Hamming distance
- Hash function
- Hypergeometric series
- Hypergraph
- Knapsack problem
- Lah number
- Large number
- Latin square
- Magic square
- Marriage theorem
- Monge array
- Moreau's necklace-counting function
- Necklace problem
- Negligible set
- Packing problem
- Permanent
- Permutation
- Pochhammer symbol
- Polyomino
- Projective plane
- Rubik's cube
- Search algorithm
- Shuffling puzzle
- Steiner system
- Stirling number
- String algorithm
- Subsequence
- Subset sum problem
- Symmetric functions
- Tower of Hanoi
- Turing tarpit
- Urn problems (probability)
- Wigner-d'Espagnat inequality
Letters
- Anagram
- Case sensitivity
- Classical ciphers
- Infinite monkey theorem
- Lexical analysis
- Lipogram
- The Library of Babel
- Literal string
- Sequence alignment
Data structure concepts
People
