List of combinatorics topics
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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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General combinatorial principles and methods
To begin with, some general principles:
- Combinatorial principles
- Trial and error, brute force search, bogosort, British Museum algorithm
- Pigeonhole principle
- Method of distinguished element
- Mathematical induction
- Recurrence relation, telescoping series
- Generating functions as an application of formal power series
- Binomial coefficients and their properties
- Double counting, combinatorial proof
- Inclusion-exclusion principle
- Möbius inversion formula
- Parity, even and odd permutations
- Incidence algebra
- Greedy algorithm
- Divide and conquer
- Dynamic programming
- Branch and bound
- Birthday attack, birthday paradox
- Floyd's cycle-finding algorithm
- Reduction to linear algebra
- Sparsity
- Weight function
- Umbral calculus
- Minimax algorithm
- Probabilistic method
- Sieve methods
- Analytic combinatorics
- Symbolic combinatorics
- Combinatorial class
- Exponential formula
Problem solving as an art
Some general theories
- Matroid
- Greedoid
- Ramsey theory
- Binomial type polynomial sequences
- Combinatorial species
Living with large numbers
- Names of large numbers, other names of large numbers, long scale
- History of large numbers
- Graham's number
- Moser's number
- Skewes' number
- Large number notations
- Large number effects
Topics
0-9
A
- Abstract simplicial complex
- Addition chain
- Alternating sign matrix
- Almost disjoint sets
- Antichain
- Arrangement of hyperplanes
- Assignment problem
- Audioactive decay
B
- Barcode
- Bell polynomials
- Bertrand's ballot theorem
- Binomial theorem
- Block design
- Boolean satisfiability problem
- Bruck-Chowla-Ryser theorem
C
- Catalan number
- Cellular automaton
- Collatz conjecture
- Combinadic
- Combination
- Combinatorial optimization
- Combinatorial search
- Constraint satisfaction problem
- Cyclic order
- Cyclotomic identity
D
- Data integrity
- De Bruijn sequence
- Deadlock
- Derangement
- Dickson's lemma
- Dinitz conjecture
- Discrete optimization
E
F
- Faà di Bruno's formula
- Factoradic
- Family of sets
- Fifteen puzzle
- Finite geometry
- Finite intersection property
G
- Game theory
- Golomb coding
- Golomb ruler
- Graeco-Latin square
- Gray code
H
- Hadamard matrix
- Hamming distance
- Hash function
- Hat problem
- Heilbronn triangle problem
- Helly family
- Hypergeometric function identities
- Hypergeometric series
- Hypergraph
I
K
L
- Lagrange inversion theorem
- Lagrange reversion theorem
- Lah number
- Large number
- Latin square
- Levenshtein distance
- Lexicographical order
- Littlewood-Offord problem
- Lubell-Yamamoto-Meshalkin inequality (known as the LYM inequality)
- Lucas chain
M
- Magic square
- Marriage theorem
- Matroid embedding
- Monge array
- Monomial order
- Moreau's necklace-counting function
- Multiset
N
O
P
- Packing problem
- Partition of a set
- Permanent
- Permutation
- Pochhammer symbol
- Polyforms
- Projective plane
- Property B
- Prüfer sequence
R
S
- Search algorithm
- Series-parallel networks problem
- Set cover problem
- Shuffling puzzle
- Sparse matrix, sparse array
- Sperner family
- Sperner's lemma
- Stable marriage problem
- Steiner system
- Stirling number
- String algorithm
- Straddling checkerboard
- Subsequence
- Subset sum problem
- Symmetric functions
- Szemerédi's theorem
T
U
- Urn problems (probability)
V
W
Y
Data structure concepts
- Data structure
- Array
- Associative array
- Deque
- List
- Queue
- Skip list
- Stack
- Tree data structure
- Automatic garbage collection
People
- Eric Temple Bell
- John Conway
- Persi Diaconis
- Paul Erdős
- Solomon Golomb
- William Timothy Gowers
- George Pólya
- Gian-Carlo Rota
- Emanuel Sperner
- Richard P. Stanley
- Endre Szemerédi
- Terence Tao
- Pal Turan