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Outline of combinatorics
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<!--... Attention: THIS IS AN OUTLINE part of the set of 830+ outlines listed at [[Wikipedia:Contents/Outlines]]. Wikipedia outlines are a special type of list article. They make up one of Wikipedia's content navigation systems See [[Wikipedia: Outlines]] and [[Wikipedia:WikiProject Outlines]] for more details. Further improvements to this outline are on the way ...--> {{Short description|1=Overview of and topical guide to combinatorics}} {{See also|Index of combinatorics articles}} '''[[Combinatorics]]''' is a branch of [[mathematics]] concerning the study of finite or [[Countable set|countable]] [[discrete mathematics|discrete]] [[Mathematical structure|structures]]. {{TOC limit|limit=2}} == Essence of combinatorics == * [[Matroid]] * [[Greedoid]] * [[Ramsey theory]] ** [[Van der Waerden's theorem]] ** [[Hales鈥揓ewett 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 method|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 == [[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 function]]s as an application of [[formal power series]] ** [[Cyclic sieving]] ** [[Schr枚dinger method]] ** [[Exponential generating function]] ** [[Stanley's reciprocity theorem]] * [[Binomial coefficient]]s and their properties * [[Combinatorial proof]] ** [[Double counting (proof technique)]] ** [[Bijective proof]] * [[Inclusion鈥揺xclusion principle]] * [[M枚bius inversion formula]] * [[Parity (mathematics)|Parity]], [[even and odd permutations]] * [[Restricted sumset|Combinatorial Nullstellensatz]] * [[Incidence algebra]] * [[Greedy algorithm]] * [[Divide and conquer algorithm]] ** [[Akra鈥揃azzi method]] * [[Dynamic programming]] * [[Branch and bound]] * [[Birthday attack]], [[birthday paradox]] * [[Floyd's cycle-finding algorithm]] * Reduction to [[linear algebra]] * [[Sparse matrix|Sparsity]] * [[Weight function]] * [[Minimax algorithm]] ** [[Alpha鈥揵eta pruning]] * [[Probabilistic method]] * [[Sieve theory|Sieve methods]] * [[Analytic combinatorics]] * [[Symbolic combinatorics]] * [[Combinatorial class]] * [[Exponential formula]] [[Talk:Exponential formula| ]] * [[Twelvefold way]] [[Talk:Twelvefold way| ]] * [[MacMahon Master theorem]] [[Talk:MacMahon Master theorem| ]] ==Data structure concepts== * [[Data structure]] ** [[Data type]] ** [[Abstract data type]] ** [[Algebraic data type]] ** [[Composite type]] * [[Array data structure|Array]] * [[Associative array]] * [[Deque]] * [[List (computing)|List]] ** [[Linked list]] * [[Queue (data structure)|Queue]] ** [[Priority queue]] * [[Skip list]] * [[Stack (data structure)|Stack]] * [[Tree data structure]] * [[Garbage collection (computer science)|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 and short scales|long scale]] * [[History of large numbers]] * [[Graham's number]] * [[Moser's number]] * [[Skewes' number]] * ''Large number notations'' ** [[Conway chained arrow notation]] ** [[Hyper4]] ** [[Knuth's up-arrow notation]] ** [[Moser polygon notation]] ** [[Steinhaus polygon notation]] * ''Large number effects'' ** [[Exponential growth]] ** [[Combinatorial explosion]] ** [[Branching factor]] ** [[Granularity]] ** [[Curse of dimensionality]] ** [[Concentration of measure]] == Persons influential in the field of combinatorics == * [[Noga Alon]] * [[George Andrews (mathematician)|George Andrews]] * [[J贸zsef Beck]] * [[Eric Temple Bell]] * [[Claude Berge]] * [[B茅la Bollob谩s]] * [[Peter Cameron (mathematician)|Peter Cameron]] * [[Louis Comtet]] * [[John Horton Conway]] ** [[On Numbers and Games]] ** [[Winning Ways for your Mathematical Plays]] * [[Persi Diaconis]] * [[Ada Dietz]] * [[Paul Erd艖s]] ** [[Erd艖s conjecture]] * [[Philippe Flajolet]] * [[Solomon Golomb]] * [[Ronald Graham (mathematician)|Ron Graham]] * [[Ben J. Green|Ben Green]] * [[William Timothy Gowers|Tim Gowers]] * [[Jeff Kahn (mathematician)|Jeff Kahn]] * [[Gil Kalai]] * [[Gyula O. H. Katona]] * [[Daniel Kleitman|Daniel J. Kleitman]] * [[Imre Leader]] * [[L谩szl贸 Lov谩sz]] * [[Fedor Petrov]] * [[George P贸lya]] * [[Vojt臎ch R枚dl]] * [[Gian-Carlo Rota]] * [[C. C. Rousseau|Cecil C. Rousseau]] * [[H. J. Ryser]] * [[Dick Schelp]] * [[Vera T. S贸s]] * [[Joel Spencer]] * [[Emanuel Sperner]] * [[Richard P. Stanley]] * [[Benny Sudakov]] * [[Endre Szemer茅di]] * [[Terence Tao]] * [[Carsten Thomassen (mathematician)|Carsten Thomassen]] * [[Jacques Touchard]] * [[P谩l Tur谩n]] * [[Bartel Leendert van der Waerden]] * [[Herbert Wilf]] * [[R. M. Wilson|Richard Wilson]] * [[Doron Zeilberger]] === Combinatorics scholars === *[[:Category:Combinatorialists]] ==Journals== * Advances in Combinatorics * [[Annals of Combinatorics]] * [[Ars Combinatoria (journal)|Ars Combinatoria]] * Australasian Journal of Combinatorics * Bulletin of the Institute of Combinatorics and Its Applications * [[Combinatorica]] * [[Combinatorics, Probability and Computing]] * [[Computational Complexity (journal)|Computational Complexity]] * Designs, Codes and Cryptography * Discrete Analysis * [[Discrete & Computational Geometry]] * Discrete Applied Mathematics * [[Discrete Mathematics (journal)|Discrete Mathematics]] * Discrete Mathematics & Theoretical Computer Science * Discrete Optimization * Discussiones Mathematicae Graph Theory * [[Electronic Journal of Combinatorics]] * [[European Journal of Combinatorics]] * [[Fibonacci Quarterly|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 * [[S茅minaire Lotharingien de Combinatoire]] * [[SIAM Journal on Discrete Mathematics]] == Prizes == * [[Euler Medal]] * [[European Prize in Combinatorics]] * [[Fulkerson Prize]] * [[K枚nig Prize]] * [[P贸lya Prize (SIAM)|P贸lya Prize]] == 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 == {{reflist}} == External links == {{sister project links|Combinatorics}} * [http://mathworld.wolfram.com/Combinatorics.html Combinatorics], a [[MathWorld]] article with many references. * [http://www.mathpages.com/home/icombina.htm Combinatorics], from a ''MathPages.com'' portal. * [https://web.archive.org/web/20090404113704/http://www.combinatorics.net/hyper/ The Hyperbook of Combinatorics], a collection of math articles links. * [http://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf The Two Cultures of Mathematics] by W. T. Gowers, article on problem solving vs theory building {{Outline footer}} [[Category:Outlines of mathematics and logic|Combinatorics]] [[Category:Outlines|Combinatorics]] [[Category:Combinatorics|+]] [[Category:Mathematics-related lists|combinatorics]]
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