Outline of combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Essence of combinatorics
- Matroid
- Greedoid
- Ramsey theory
- Van der Waerden's theorem
- Hales–Jewett theorem
- Umbral calculus, binomial type polynomial sequences
- Combinatorial species
Branches of combinatorics
- Algebraic combinatorics
- Analytic combinatorics
- Arithmetic combinatorics
- Combinatorics on words
- Combinatorial design theory
- Enumerative combinatorics
- Extremal combinatorics
- Geometric combinatorics
- Graph theory
- Infinitary combinatorics
- Matroid theory
- Order theory
- Partition theory
- Probabilistic combinatorics
- Topological combinatorics
Multi-disciplinary fields that include combinatorics
- Coding theory
- Combinatorial optimization
- Combinatorics and dynamical systems
- Combinatorics and physics
- Discrete geometry
- Finite geometry
- Phylogenetics
History of combinatorics
General combinatorial principles and methods
- 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
- MacMahon Master theorem
Data structure concepts
- Data structure
- Array
- Associative array
- Deque
- List
- Queue
- Skip list
- Stack
- Tree data structure
- Automatic garbage collection
Problem solving as an art
- Heuristic
- Inductive reasoning
- How to Solve It
- Creative problem solving
- Morphological analysis (problem-solving)
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
Persons influential in the field of combinatorics
- Noga Alon
- George Andrews
- József Beck
- Eric Temple Bell
- Claude Berge
- Béla Bollobás
- Peter Cameron
- Louis Comtet
- John Horton Conway
- Persi Diaconis
- Ada Dietz
- Paul Erdős
- Philippe Flajolet
- Solomon Golomb
- Ron Graham
- Ben Green
- Tim Gowers
- Jeff Kahn
- Gil Kalai
- Gyula O. H. Katona
- Daniel J. Kleitman
- Imre Leader
- László Lovász
- Fedor Petrov
- George Pólya
- Vojtěch Rödl
- Gian-Carlo Rota
- Cecil C. Rousseau
- H. J. Ryser
- Dick Schelp
- Vera T. Sós
- Joel Spencer
- Emanuel Sperner
- Richard P. Stanley
- Benny Sudakov
- Endre Szemerédi
- Terence Tao
- Carsten Thomassen
- Jacques Touchard
- Pál Turán
- Bartel Leendert van der Waerden
- Herbert Wilf
- Richard Wilson
- Doron Zeilberger
Combinatorics scholars
Journals
- Advances in Combinatorics
- 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 Analysis
- 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 Lotharingien de Combinatoire
- SIAM Journal on Discrete Mathematics
Prizes
See also
- List of factorial and binomial topics
- List of partition topics
- List of permutation topics
- List of puzzle topics.
- List of formal language and literal string topics
References
External links
Combinatorics at Wikipedia's sister projects
Definitions from Wiktionary
Media from Commons
News from Wikinews
Quotations from Wikiquote
Texts from Wikisource
Textbooks from Wikibooks
Resources from Wikiversity
- Combinatorics, a MathWorld article with many references.
- Combinatorics, from a MathPages.com portal.
- The Hyperbook of Combinatorics, a collection of math articles links.
- The Two Cultures of Mathematics by W. T. Gowers, article on problem solving vs theory building