List of combinatorics topics.html |
| | | ca | | | de | | | en | | | es | | | fr | | | it | | | nl | | | no | | | pl | | | pt | | | ru | | | ro | | | fi | | | sv | | | tr | | | vo | | |
| |  |
This is a list of combinatorics topics.
A few decades ago it might have been said that combinatorics is little more than 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.
Contents |
General combinatorial principles and methods
To begin with, some general principles:
- Fundamental theorem of combinatorial enumeration
- 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
- Combinatorial proof
- Inclusion-exclusion principle
- Möbius inversion formula
- Parity, even and odd permutations
- Combinatorial Nullstellensatz
- Incidence algebra
- Greedy algorithm
- Divide and conquer algorithm
- Dynamic programming
- Branch and bound
- Birthday attack, birthday paradox
- Floyd's cycle-finding algorithm
- Reduction to linear algebra
- Sparsity
- Weight function
- Minimax algorithm
- Probabilistic method
- Sieve methods
- Analytic combinatorics
- Symbolic combinatorics
- Combinatorial class
- Exponential formula
- Twelvefold way
Problem solving as an art
Some general theories
- Matroid
- Greedoid
- Ramsey theory
- Van der Waerden's theorem
- Hales-Jewett theorem
- Umbral calculus, binomial type polynomial sequences
- Combinatorial species
Living with large numbers
- 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 in combinatorics: alphabetical list
0-9
- Binary matrix (i.e. (0,1)-matrix)
A
- Abstract simplicial complex
- Addition chain
- Algebraic combinatorics
- 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
- Block walking
- Boolean satisfiability problem
- Bracelet (combinatorics)
- Bruck-Chowla-Ryser theorem
C
- Catalan number
- Cellular automaton
- Collatz conjecture
- Combinadic
- Combination
- Combinatorial design
- Combinatorial optimization
- Combinatorial search
- Constraint satisfaction problem
- Cycles and fixed points
- Cyclic order
- Cyclic permutation
- Cyclotomic identity
D
- Data integrity
- De Bruijn sequence
- Deadlock
- Delannoy number
- Derangement
- Dickson's lemma
- Dinitz conjecture
- Discrete optimization
- Dobinski's formula
E
F
- Faà di Bruno's formula
- Factoradic
- Family of sets
- Faulhaber's formula
- Fifteen puzzle
- Finite geometry
- Finite intersection property
G
- Game theory
- Golomb coding
- Golomb ruler
- Graeco-Latin square
- Gray code
H
- Hadamard matrices
- 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
- Motzkin number
- Multiplicities of entries in Pascal's triangle
- Multiset
- Munkres' assignment algorithm
N
O
P
- Packing problem
- Partition of a set
- Permanent
- Permutation
- Pochhammer symbol
- Polyforms
- Projective plane
- Property B
- Prüfer sequence
Q
- q-analog
- q-binomial theorem—see Gaussian binomial
- q-derivative
- q-series
- q-theta function
- q-Vandermonde identity
R
S
- Schröder number
- Search algorithm
- Sequences with zero autocorrelation function
- Series-parallel networks problem
- Set cover problem
- Shuffling puzzle
- Small set (combinatorics)
- 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
- Noga Alon
- George Andrews
- Eric Temple Bell
- Belá Bollobás
- Peter Cameron
- Louis Comtet
- John Horton Conway
- Persi Diaconis
- Ada Dietz
- Paul Erdős
- Solomon Golomb
- Ben Green
- Tim Gowers
- Gyula O. H. Katona
- Imré Leader
- Luke Pebody
- George Pólya
- Gian-Carlo Rota
- Cecil C. Rousseau
- Dick Schelp
- Vèra T. Sôs
- Joel Spencer
- Emanuel Sperner
- Richard P. Stanley
- Endre Szemerédi
- Terence Tao
- Jacques Touchard
- Bartel Leendert van der Waerden
- Herbert Wilf
- Doron Zeilberger
Journals
- Annals of Combinatorics
- Ars Combinatoria
- Australasian Journal of Combinatorics
- Bulletin of the Institute of Combinatorics and Its Applications
- Combinatorica
- Combinatorics, Probability and Computing
- Computational Complexity
- Designs, Codes and Cryptography
- Discrete and Computational Geometry
- Discrete Applied Mathematics
- Discrete Mathematics
- Discrete Mathematics & Theoretical Computer Science
- Discrete Optimization
- Discussiones Mathematicae Graph Theory
- Electronic Journal of Combinatorics
- European Journal of Combinatorics
- The Fibonacci Quarterly
- Finite Fields and Their Applications
- Geombinatorics
- Graphs and Combinatorics
- Integers, Electronic Journal of Combinatorial Number Theory
- Journal of Algebraic Combinatorics
- Journal of Automata Languages and Combinatorics
- Journal of Combinatorial Designs
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Journal of Combinatorial Optimization
- Journal of Combinatorial Theory, Series A
- Journal of Combinatorial Theory, Series B
- Journal of Complexity
- Journal of Cryptology
- Journal of Graph Algorithms and Applications
- Journal of Graph Theory
- Journal of Integer Sequences (Electronic)
- Journal of Mathematical Chemistry
- Online Journal of Analytic Combinatorics
- Optimization Methods and Software
- The Ramanujan Journal
- Séminaire Lostharingien de Combinatoire
- SIAM Journal on Discrete Mathematics