countable
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers ...
discrete
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
*Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
*Discrete group, a g ...
structures
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
.
Essence of combinatorics
*
Matroid
In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being ...
*
Greedoid
In combinatorics, a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Hassler Whitney, Whitney in 1935 to study planar graphs and was later used by Jack Edmonds, Edmonds to characterize a ...
*
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask ...
**
Van der Waerden's theorem
Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden's theorem states that for any given positive integers ''r'' and ''k'', there is some number ''N'' such that if the integers are colored, ea ...
Umbral calculus
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them. These techniques were introduced by John Blis ...
,
binomial type
In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers \left\ in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities
:p_ ...
polynomial sequences
*
Combinatorial species
In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for deriving the generating functions of discrete structures, which allows one to not merely count these structures but give bijective proofs invol ...
Analytic combinatorics
In combinatorics, the symbolic method is a technique for counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions. The method is mostly associated with Philippe Flajolet an ...
*
Arithmetic combinatorics In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
Scope
Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations (ad ...
*
Combinatorics on words
Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words af ...
Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infin ...
Graph theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
*
Infinitary combinatorics In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets.
Some of the things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom.
Re ...
*
Matroid theory
In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being ...
*
Order theory
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article int ...
Topological combinatorics The mathematical discipline of topological combinatorics is the application of topological and algebro-topological methods to solving problems in combinatorics.
History
The discipline of combinatorial topology used combinatorial concepts in top ...
Multi-disciplinary fields that include combinatorics
*
Coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied ...
*
Combinatorial optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combi ...
*
Combinatorics and dynamical systems The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of ...
*
Combinatorics and physics Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.
Overview
:"Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretica ...
*
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic ge ...
*
Finite geometry
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marke ...
*
Phylogenetics
In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups ...
Combinatorial principles In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used.
The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. B ...
*
Trial and error
Trial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued until success, or until the practicer stops trying.
According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (18 ...
bogosort
In computer science, bogosort (also known as permutation sort, stupid sort, slowsort or bozosort) is a sorting algorithm based on the generate and test paradigm. The function successively generates permutations of its input until it finds one t ...
,
British Museum algorithm
The British Museum algorithm is a general approach to finding a solution by checking all possibilities one by one, beginning with the smallest. The term refers to a conceptual, not a practical, technique where the number of possibilities is enor ...
*
Pigeonhole principle
In mathematics, the pigeonhole principle states that if items are put into containers, with , then at least one container must contain more than one item. For example, if one has three gloves (and none is ambidextrous/reversible), then there mu ...
*
Method of distinguished element
In the mathematical field of enumerative combinatorics, identities are sometimes established by arguments that rely on singling out one "distinguished element" of a set.
Definition
Let \mathcal be a family of subsets of the set A and let x \in ...
*
Mathematical induction
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help ...
*
Recurrence relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...
,
telescoping series
In mathematics, a telescoping series is a series whose general term t_n can be written as t_n=a_n-a_, i.e. the difference of two consecutive terms of a sequence (a_n).
As a consequence the partial sums only consists of two terms of (a_n) after c ...
Cyclic sieving In combinatorial mathematics, cyclic sieving is a phenomenon by which evaluating a generating function for a finite set at roots of unity counts symmetry classes of objects acted on by a cyclic group.
Definition
Let ''C'' be a cyclic group gene ...
Exponential generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series ...
**
Stanley's reciprocity theorem
In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generatin ...
Combinatorial proof In mathematics, the term ''combinatorial proof'' is often used to mean either of two types of mathematical proof:
* A proof by double counting. A combinatorial identity is proven by counting the number of elements of some carefully chosen set in t ...
Bijective proof
In combinatorics, bijective proof is a proof technique for proving that two sets have equally many elements, or that the sets in two combinatorial classes have equal size, by finding a bijective function that maps one set one-to-one onto the othe ...
*
Inclusion–exclusion principle
In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
: , A \cu ...
*
Möbius inversion formula
In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius.
A large gener ...
even and odd permutations
In mathematics, when ''X'' is a finite set with at least two elements, the permutations of ''X'' (i.e. the bijective functions from ''X'' to ''X'') fall into two classes of equal size: the even permutations and the odd permutations. If any total ...
Incidence algebra In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set
and commutative ring with unity. Subalgebras called reduced incidence algebras give a natural constructi ...
*
Greedy algorithm
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally ...
*
Divide and conquer algorithm
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved direc ...
**
Akra–Bazzi method
In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantia ...
*
Dynamic programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. ...
*
Branch and bound
Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solut ...
birthday paradox
In probability theory, the birthday problem asks for the probability that, in a set of randomly chosen people, at least two will share a birthday. The birthday paradox is that, counterintuitively, the probability of a shared birthday exceeds 5 ...
linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrices ...
*
Sparsity
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b ...
*
Weight function
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is ...
*
Minimax algorithm
Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for ''mini''mizing the possible loss for a worst case (''max''imum loss) scenario. When de ...
**
Alpha–beta pruning
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player games ...
*
Probabilistic method
The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects fr ...
Analytic combinatorics
In combinatorics, the symbolic method is a technique for counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions. The method is mostly associated with Philippe Flajolet an ...
Combinatorial class In mathematics, a combinatorial class is a countable set of mathematical objects, together with a size function mapping each object to a non-negative integer, such that there are finitely many objects of each size.
Counting sequences and isomorphis ...
*
Exponential formula In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected st ...
*
Twelvefold way
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of ...
Abstract data type
In computer science, an abstract data type (ADT) is a mathematical model for data types. An abstract data type is defined by its behavior (semantics) from the point of view of a ''user'', of the data, specifically in terms of possible values, pos ...
**
Algebraic data type
In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite type, i.e., a type formed by combining other types.
Two common classes of algebraic types are product types (i.e., ...
**
Composite type
In computer science, a composite data type or compound data type is any data type which can be constructed in a program using the programming language's primitive data types and other composite types. It is sometimes called a structure or aggreg ...
*
Array
An array is a systematic arrangement of similar objects, usually in rows and columns.
Things called an array include:
{{TOC right
Music
* In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...
*
Associative array
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms an ...
*
Deque
In computer science, a double-ended queue (abbreviated to deque, pronounced ''deck'', like "cheque") is an abstract data type that generalizes a queue, for which elements can be added to or removed from either the front (head) or back (tail). ...
*
List
A ''list'' is any set of items in a row. List or lists may also refer to:
People
* List (surname)
Organizations
* List College, an undergraduate division of the Jewish Theological Seminary of America
* SC Germania List, German rugby unio ...
Queue __NOTOC__
Queue () may refer to:
* Queue area, or queue, a line or area where people wait for goods or services
Arts, entertainment, and media
*''ACM Queue'', a computer magazine
* ''The Queue'' (Sorokin novel), a 1983 novel by Russian author ...
Skip list
In computer science, a skip list (or skiplist) is a probabilistic data structure that allows \mathcal(\log n) average complexity for search as well as \mathcal(\log n) average complexity for insertion within an ordered sequence of n elements. T ...
Tree data structure
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be c ...
*
Automatic garbage collection
In computer science, garbage collection (GC) is a form of automatic memory management. The ''garbage collector'' attempts to reclaim memory which was allocated by the program, but is no longer referenced; such memory is called '' garbage''. ...
Problem solving as an art
*
Heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate ...
How to Solve It
''How to Solve It'' (1945) is a small volume by mathematician George Pólya describing methods of problem solving.
Four principles
''How to Solve It'' suggests the following steps when solving a mathematical problem:
# First, you have to ''und ...
''
*
Creative problem solving
Creative problem-solving (CPS) is the mental process of searching for an original and previously unknown solution to a problem. To qualify, the solution must be novel and reached independently. The creative problem-solving process was originally de ...
*
Morphological analysis (problem-solving) Morphological analysis is the analysis of morphology in various fields
* Morphological analysis (problem-solving) or general morphological analysis, a method for exploring all possible solutions to a multi-dimensional, non-quantified problem
* An ...
Living with large numbers
*
Names of large numbers
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-E ...
History of large numbers
Different cultures used different traditional numeral systems for naming large numbers. The extent of large numbers used varied in each culture. Two interesting points in using large numbers are the confusion on the term billion and milliard in ma ...
Skewes' number
In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which
:\pi(x) > \operatorname(x),
where is the prime-counting function ...
* ''Large number notations''
**
Conway chained arrow notation
Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2\to3\to4\to5\to6.
As wit ...
Knuth's up-arrow notation
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.
In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperati ...
Exponential growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a ...
**
Combinatorial explosion
In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion is sometimes used to ...
**
Branching factor
In computing, tree data structures, and game theory, the branching factor is the number of children at each node, the outdegree. If this value is not uniform, an ''average branching factor'' can be calculated.
For example, in chess, if a "no ...
**
Granularity
Granularity (also called graininess), the condition of existing in granules or grains, refers to the extent to which a material or system is composed of distinguishable pieces. It can either refer to the extent to which a larger entity is sub ...
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Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. T ...
**
Concentration of measure
In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that "A random v ...
Persons influential in the field of combinatorics
*
Noga Alon
Noga Alon ( he, נוגה אלון; born 17 February 1956) is an Israeli mathematician and a professor of mathematics at Princeton University noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of ...
József Beck
József Beck (Budapest, Hungary, February 14, 1952) is a Harold H. Martin Professor of Mathematics at Rutgers University.
His contributions to combinatorics include the partial colouring lemma and the Beck–Fiala theorem in '' discrepancy th ...
*
Eric Temple Bell
Eric Temple Bell (7 February 1883 – 21 December 1960) was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction as John Tain ...
*
Claude Berge
Claude Jacques Berge (5 June 1926 – 30 June 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory.
Biography and professional history
Claude Berge's parents were André Berge and Geneviève ...
*
Béla Bollobás
Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Pa ...
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...
**
On Numbers and Games
''On Numbers and Games'' is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpre ...
Persi Diaconis
Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.
He is particularly know ...
Erdős conjecture
Erdős, Erdos, or Erdoes is a Hungarian surname.
People with the surname include:
* Ágnes Erdős (born 1950), Hungarian politician
* Brad Erdos (born 1990), Canadian football player
* Éva Erdős (born 1964), Hungarian handball player
* Józ ...
*
Philippe Flajolet
Philippe Flajolet (; 1 December 1948 – 22 March 2011) was a French computer scientist.
Biography
A former student of École Polytechnique, Philippe Flajolet received his PhD in computer science from University Paris Diderot in 1973 and state ...
Jeff Kahn
Jeffry Ned Kahn is a professor of mathematics at Rutgers University notable for his work in combinatorics.
Education
Kahn received his Ph.D. from Ohio State University in 1979 after completing his dissertation under his advisor Dijen K. Ray-Cha ...
*
Gil Kalai
Gil Kalai (born 1955) is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, Israel, Professor of Computer Science at the Interdisciplinary Center, Herzliya, and adjunct Professor of mathematics ...
*
Gyula O. H. Katona
Gyula O. H. Katona (born 16 March 1941 in Budapest) is a Hungarian mathematician known for his work in combinatorial set theory, and especially for the Kruskal–Katona theorem
In algebraic combinatorics, the Kruskal–Katona theorem gives a co ...
Imre Leader
Imre Bennett Leader is a British Othello player, employed as a professor of pure mathematics at Cambridge University.
As a child, he was a pupil at the private St Paul's School and won a silver medal on the British team at the 1981 Internatio ...
*
László Lovász
László Lovász (; born March 9, 1948) is a Hungarian mathematician and professor emeritus at Eötvös Loránd University, best known for his work in combinatorics, for which he was awarded the 2021 Abel Prize jointly with Avi Wigderson. He wa ...
George Pólya
George Pólya (; hu, Pólya György, ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamenta ...
*
Vojtěch Rödl
Vojtěch Rödl (born 1 April 1949) is a Czech American mathematician, Samuel Candler Dobbs Professor at Emory University. He is noted for his contributions mainly to combinatorics having authored hundreds of research papers.
Academic Background ...
*
Gian-Carlo Rota
Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, proba ...
H. J. Ryser
Herbert John Ryser (July 28, 1923 – July 12, 1985) was a professor of mathematics, widely regarded as one of the major figures in combinatorics in the 20th century.Dick Schelp
*
Vera T. Sós
Vera T. Sós (born September 11, 1930) is a Hungarian mathematician, specializing in number theory and combinatorics. She was a student and close collaborator of both Paul Erdős and Alfréd Rényi. She also collaborated frequently with her h ...
*
Joel Spencer
Joel Spencer (born April 20, 1946) is an American mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, da ...
*
Emanuel Sperner
Emanuel Sperner (9 December 1905 – 31 January 1980) was a German mathematician, best known for two theorems. He was born in Waltdorf (near Neiße, Upper Silesia, now Nysa, Poland), and died in Sulzburg-Laufen, West Germany. He was a student at ...
*
Richard P. Stanley
Richard Peter Stanley (born June 23, 1944) is an Emeritus Professor of Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. From 2000 to 2010, he was the Norman Levinson Professor of Applied Mathematics. He r ...
*
Benny Sudakov
Benny Sudakov (born October 1969) is an Israeli mathematician, who works mainly on Hungarian-style combinatorics.
He was born in Tbilissi, Georgia, and completed his undergraduate studies at Tbilisi State University in 1990. After emigrating to ...
*
Endre Szemerédi
Endre Szemerédi (; born August 21, 1940) is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science ...
Carsten Thomassen Carsten Thomassen may refer to:
* Carsten Thomassen (mathematician)
* Carsten Thomassen (journalist)
Carsten Thomassen (15 May 1969 – 14 January 2008) was a Norwegian journalist, political commentator and war correspondent for the Norwegian ...
Pál Turán
Pál Turán (; 18 August 1910 – 26 September 1976) also known as Paul Turán, was a Hungarian mathematician who worked primarily in extremal combinatorics. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting ...
*
Bartel Leendert van der Waerden
Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics.
Biography
Education and early career
Van der Waerden learned advanced mathematics at the University of Amster ...
*
Herbert Wilf
Herbert Saul Wilf (June 13, 1931 – January 7, 2012) was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylv ...
Doron Zeilberger
Doron Zeilberger (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics.
Education and career
He received his doctorate from the Weizmann Institute of Science in 1976, u ...
* Advances in Combinatorics
* Annals of Combinatorics
* Ars Combinatoria
* Australasian Journal of Combinatorics
* Bulletin of the Institute of Combinatorics and Its Applications
*
Combinatorica
''Combinatorica'' is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science. It started in 1981, with László Babai and László Lovász as the editors-in-chief with Paul Erdős as honora ...
*
Combinatorics, Probability and Computing
''Combinatorics, Probability and Computing'' is a peer-reviewed scientific journal in mathematics published by Cambridge University Press. Its editor-in-chief is Béla Bollobás ( DPMMS and University of Memphis).
History
The journal was estab ...
Discrete and Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geome ...
Electronic Journal of Combinatorics
The ''Electronic Journal of Combinatorics'' is a peer-reviewed open access scientific journal covering research in combinatorial mathematics.
The journal was established in 1994 by Herbert Wilf (University of Pennsylvania) and Neil Calkin ( Ge ...
Geombinatorics
Alexander Soifer is a Russian-born American mathematician and mathematics author. His works include over 400 articles and 13 books.
Soifer obtained his Ph.D. in 1973 and has been a professor of mathematics at the University of Colorado since 19 ...
*
Graphs and Combinatorics
''Graphs and Combinatorics'' (ISSN 0911-0119, abbreviated ''Graphs Combin.'') is a peer-reviewed academic journal in graph theory, combinatorics, and discrete geometry published by Springer Japan. Its editor-in-chief is Katsuhiro Ota of Keio Univ ...
Journal of Automata, Languages and Combinatorics
The ''Journal of Automata, Languages and Combinatorics'' (JALC) is a peer-reviewed scientific journal of computer science. It was established in 1965 as the ''Journal of Information Processing and Cybernetics'' (German: ''Elektronische Informations ...
* Journal of Combinatorial Designs
* Journal of Combinatorial Mathematics and Combinatorial Computing
* Journal of Combinatorial Optimization
*
Journal of Combinatorial Theory, Series A
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applicatio ...
Journal of Cryptology
The ''Journal of Cryptology'' () is a scientific journal in the field of cryptology and cryptography. The journal is published quarterly by the International Association for Cryptologic Research
International is an adjective (also used as a nou ...
*
Journal of Graph Algorithms and Applications
The ''Journal of Graph Algorithms and Applications'' is an open access peer-reviewed scientific journal covering the subject of graph algorithms and graph drawing. The journal was established in 1997 and the editor-in-chief is Giuseppe Liotta (U ...
*
Journal of Graph Theory
The ''Journal of Graph Theory'' is a peer-reviewed mathematics journal specializing in graph theory and related areas, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs.
The ...
* Journal of Integer Sequences (Electronic)
* Journal of Mathematical Chemistry
* Online Journal of Analytic Combinatorics
* Optimization Methods and Software
* The Ramanujan Journal
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Séminaire Lotharingien de Combinatoire
The ''Séminaire Lotharingien de Combinatoire'' (English: ''Lotharingian Seminar of Combinatorics'') is a peer-reviewed academic journal specialising in combinatorial mathematics, named after Lotharingia.
It has existed since 1980 as a regular jo ...
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SIAM Journal on Discrete Mathematics
'' SIAM Journal on Discrete Mathematics'' is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM). The journal includes articles on pure and applied discrete mathematics. It was estab ...
Prizes
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Euler Medal
The Institute of Combinatorics and its Applications (ICA) is an international scientific organization formed in 1990 to increase the visibility and influence of the combinatorial community. In pursuit of this goal, the ICA sponsors conferences, ...
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European Prize in Combinatorics The European Prize in Combinatorics is a prize for research in combinatorics, a mathematical discipline, which is awarded biennially at Eurocomb, the European conference on combinatorics, graph theory, and applications.. The prize was first awarde ...
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Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e ...
List of factorial and binomial topics {{Short description, none
This is a list of factorial and binomial topics in mathematics. See also binomial (disambiguation).
* Abel's binomial theorem
* Alternating factorial
*Antichain
*Beta function
*Bhargava factorial
*Binomial coefficient
**P ...
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List of partition topics
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are
* partition of a set or an ordered partition of a set,
* partition of a graph,
* partition of an integer,
* ...
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List of permutation topics
This is a list of topics on mathematical permutations.
Particular kinds of permutations
*Alternating permutation
*Circular shift
*Cyclic permutation
*Derangement
*Even and odd permutations—see Parity of a permutation
*Josephus permutation ...
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List of puzzle topics
{{Puzzles , lists
This is a list of puzzle topics, by Wikipedia page.
* Acrostic (puzzle), Acrostic
* Anagram
* Back from the klondike
* Ball-in-a-maze puzzle
* Brain teaser
* Burr puzzle
* Chess problem
* Chess puzzle
* Computer puzzle game
* C ...
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List of formal language and literal string topics {{Short description, none
This is a list of formal language and literal string topics, by Wikipedia page.
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Formal languages
* Abstract syntax tree
* Backus-Naur form
* Categorial grammar
* Chomsky hierarchy
* Concatenation
* Context-free gra ...
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Di ...