
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. ==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 **Schrödinger method **exponential generating function **Stanley's reciprocity theorem *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 (computer science) **Akra-Bazzi method *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 **Alpha-beta pruning *Probabilistic method *Sieve methods *Analytic combinatorics *Symbolic combinatorics *Combinatorial class *Exponential formula Talk:Exponential formula ==Problem solving as an art== *Heuristic *Inductive reasoning *''How to Solve It'' *Creative problem solving *''Art of Problem Solving'' ==Some general theories== *Matroid *Greedoid *Ramsey theory **Van der Waerden's theorem **Hales-Jewett theorem *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'' **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 ==Topics== ===0-9=== *(0,1) matrix ===A=== *Abstract simplicial complex *Addition chain **Scholz conjecture *Alternating sign matrix *Almost disjoint sets *Antichain *Arrangement of hyperplanes *Assignment problem *Audioactive decay ===B=== *Barcode **Matrix code **QR Code **Universal Product Code *Bell polynomials *Bertrand's ballot theorem *Binomial theorem *Block design *Boolean satisfiability problem **2-satisfiability **Boolean satisfiability problem *Bruck-Chowla-Ryser theorem ===C=== *Catalan number *Cellular automaton **Conway's Game of Life *Collatz conjecture *Combinadic *Combination *Combinatorial optimization *Combinatorial search *Constraint satisfaction problem *Cyclic order *Cyclotomic identity ===D=== *Data integrity **Alternating bit protocol **Checksum **Cyclic redundancy check ***Luhn formula **Error detection ***Error-detecting code ***Error-detecting system **Message digest **Redundancy check **Summation check *De Bruijn sequence *Deadlock **Dining philosophers problem **Mutual exclusion **Rendezvous problem *Derangement *Dickson's lemma *Dinitz conjecture *Discrete optimization ===E=== *Eight queens puzzle *Entropy coding *Enumeration **Algebraic enumeration **Combinatorial enumeration **Burnside's lemma *Erdös-Ko-Rado theorem *Euler number ===F=== *Faà di Bruno's formula *Factoradic *Family of sets *Fifteen puzzle *Finite geometry *Finite intersection property ===G=== *Game theory **Combinatorial game theory ***Combinatorial game theory (history) ***Combinatorial game theory (pedagogy) ***Star (game) ***Zero game, fuzzy game **Dots and Boxes **Impartial game ***Digital sum ***Nim ***Nimber ***Sprague-Grundy theorem **Partizan game **Solved board games **Col game **Sim **Sprouts (game) **Surreal numbers **Transposition table **Black Path Game **Sylver coinage *Golomb coding *Golomb ruler *Graeco-Latin square *Gray code ===H=== *Hadamard matrix *Hamming distance *Hash function **Hash collision **Perfect hash function *Hat problem *Heilbronn triangle problem *Helly family *Hypergeometric function identities *Hypergeometric series *Hypergraph ===I=== *Incidence structure *Integer partition **Ferrers graph ===K=== *Kakeya needle problem *Knapsack problem *Kruskal-Katona theorem ===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 **Perfect matching *Matroid embedding *Monge array *Monomial order *Moreau's necklace-counting function *Multiset ===N=== *Necklace problem *Negligible set **Almost all **Almost everywhere **Null set ===O=== *Ordered partition of a set ===P=== *Packing problem **Bin packing problem *Partition of a set **Noncrossing partition *Permanent *Permutation **Permutation matrix **Permutations and combinations **Josephus permutation **Shuffling playing cards *Pochhammer symbol *Polyforms **Polycubes ***Soma cube **Polyiamonds **Polyominoes ***Hexominoes ***Pentominoes ***Tetrominoes **Polysquare puzzle *Projective plane *Property B *Prüfer sequence ===R=== *Rubik's cube **How to solve the Rubik's Cube **Optimal solutions for Rubik's Cube **Rubik's Revenge ===S=== *Search algorithm **Binary search **Interpolation search **Linear search **Local search **String searching algorithm ***Aho-Corasick algorithm ***Fuzzy string searching ***grep, agrep, wildcard character ***Knuth-Morris-Pratt 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 **Stirling transform *String algorithm *Straddling checkerboard *Subsequence **Longest-common subsequence problem ***Optimal-substructure *Subset sum problem *Symmetric functions *Szemerédi's theorem ===T=== *Thue-Morse sequence *Tower of Hanoi *Turing tarpit ===U=== *Urn problems (probability) ===V=== *Vandermonde's identity ===W=== *Weighted round robin **Deficit round robin *Wigner-d'Espagnat inequality ===Y=== *Young tableau ==Data structure concepts== *Data structure **Data type **Abstract data type **Algebraic data type **Composite type *Array *Associative array *Deque *List **Linked list *Queue **Priority queue *Skip list *Stack (computing) *Tree data structure *Garbage collection (computer science) ==People== *Eric Temple Bell *John Conway **On Numbers and Games **Winning Ways for your Mathematical Plays *Persi Diaconis *Paul Erdös **Erdös conjecture *Solomon Golomb *William Timothy Gowers *George Pólya *Gian-Carlo Rota *Emanuel Sperner *Richard P. Stanley *Endre Szemerédi *Terence Tao *Pal Turan ==Publications== *''Geombinatorics'' ==See also== * list of factorial and binomial topics * list of partition topics * list of puzzle topics. * list of formal language and literal string topics Topic listsCombinatorics
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Words begining with List_of_combinatorics_topics:
List_of_combinatorics_topics
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. ==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 **Schrödinger method **exponential generating function **Stanley's reciprocity theorem *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 (computer science) **Akra-Bazzi method *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 **Alpha-beta pruning *Probabilistic method *Sieve methods *Analytic combinatorics *Symbolic combinatorics *Combinatorial class *Exponential formula Talk:Exponential formula ==Problem solving as an art== *Heuristic *Inductive reasoning *''How to Solve It'' *Creative problem solving *''Art of Problem Solving'' ==Some general theories== *Matroid *Greedoid *Ramsey theory **Van der Waerden's theorem **Hales-Jewett theorem *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'' **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 ==Topics== ===0-9=== *(0,1) matrix ===A=== *Abstract simplicial complex *Addition chain **Scholz conjecture *Alternating sign matrix *Almost disjoint sets *Antichain *Arrangement of hyperplanes *Assignment problem *Audioactive decay ===B=== *Barcode **Matrix code **QR Code **Universal Product Code *Bell polynomials *Bertrand's ballot theorem *Binomial theorem *Block design *Boolean satisfiability problem **2-satisfiability **Boolean satisfiability problem *Bruck-Chowla-Ryser theorem ===C=== *Catalan number *Cellular automaton **Conway's Game of Life *Collatz conjecture *Combinadic *Combination *Combinatorial optimization *Combinatorial search *Constraint satisfaction problem *Cyclic order *Cyclotomic identity ===D=== *Data integrity **Alternating bit protocol **Checksum **Cyclic redundancy check ***Luhn formula **Error detection ***Error-detecting code ***Error-detecting system **Message digest **Redundancy check **Summation check *De Bruijn sequence *Deadlock **Dining philosophers problem **Mutual exclusion **Rendezvous problem *Derangement *Dickson's lemma *Dinitz conjecture *Discrete optimization ===E=== *Eight queens puzzle *Entropy coding *Enumeration **Algebraic enumeration **Combinatorial enumeration **Burnside's lemma *Erdös-Ko-Rado theorem *Euler number ===F=== *Faà di Bruno's formula *Factoradic *Family of sets *Fifteen puzzle *Finite geometry *Finite intersection property ===G=== *Game theory **Combinatorial game theory ***Combinatorial game theory (history) ***Combinatorial game theory (pedagogy) ***Star (game) ***Zero game, fuzzy game **Dots and Boxes **Impartial game ***Digital sum ***Nim ***Nimber ***Sprague-Grundy theorem **Partizan game **Solved board games **Col game **Sim **Sprouts (game) **Surreal numbers **Transposition table **Black Path Game **Sylver coinage *Golomb coding *Golomb ruler *Graeco-Latin square *Gray code ===H=== *Hadamard matrix *Hamming distance *Hash function **Hash collision **Perfect hash function *Hat problem *Heilbronn triangle problem *Helly family *Hypergeometric function identities *Hypergeometric series *Hypergraph ===I=== *Incidence structure *Integer partition **Ferrers graph ===K=== *Kakeya needle problem *Knapsack problem *Kruskal-Katona theorem ===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 **Perfect matching *Matroid embedding *Monge array *Monomial order *Moreau's necklace-counting function *Multiset ===N=== *Necklace problem *Negligible set **Almost all **Almost everywhere **Null set ===O=== *Ordered partition of a set ===P=== *Packing problem **Bin packing problem *Partition of a set **Noncrossing partition *Permanent *Permutation **Permutation matrix **Permutations and combinations **Josephus permutation **Shuffling playing cards *Pochhammer symbol *Polyforms **Polycubes ***Soma cube **Polyiamonds **Polyominoes ***Hexominoes ***Pentominoes ***Tetrominoes **Polysquare puzzle *Projective plane *Property B *Prüfer sequence ===R=== *Rubik's cube **How to solve the Rubik's Cube **Optimal solutions for Rubik's Cube **Rubik's Revenge ===S=== *Search algorithm **Binary search **Interpolation search **Linear search **Local search **String searching algorithm ***Aho-Corasick algorithm ***Fuzzy string searching ***grep, agrep, wildcard character ***Knuth-Morris-Pratt 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 **Stirling transform *String algorithm *Straddling checkerboard *Subsequence **Longest-common subsequence problem ***Optimal-substructure *Subset sum problem *Symmetric functions *Szemerédi's theorem ===T=== *Thue-Morse sequence *Tower of Hanoi *Turing tarpit ===U=== *Urn problems (probability) ===V=== *Vandermonde's identity ===W=== *Weighted round robin **Deficit round robin *Wigner-d'Espagnat inequality ===Y=== *Young tableau ==Data structure concepts== *Data structure **Data type **Abstract data type **Algebraic data type **Composite type *Array *Associative array *Deque *List **Linked list *Queue **Priority queue *Skip list *Stack (computing) *Tree data structure *Garbage collection (computer science) ==People== *Eric Temple Bell *John Conway **On Numbers and Games **Winning Ways for your Mathematical Plays *Persi Diaconis *Paul Erdös **Erdös conjecture *Solomon Golomb *William Timothy Gowers *George Pólya *Gian-Carlo Rota *Emanuel Sperner *Richard P. Stanley *Endre Szemerédi *Terence Tao *Pal Turan ==Publications== *''Geombinatorics'' ==See also== * list of factorial and binomial topics * list of partition topics * list of puzzle topics. * list of formal language and literal string topics Topic listsCombinatorics
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