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37 relations: Algebraic combinatorics, Algebraic enumeration, Anders Björner, Asymptotic analysis, Burnside's lemma, Cambridge University Press, Cartesian product, Catalan number, Closed-form expression, Combination, Combinatorial explosion, Combinatorial game theory, Combinatorial principles, Combinatorial species, Combinatorics, Doron Zeilberger, Encyclopædia Britannica Eleventh Edition, Factorial, Generating function, Inclusion–exclusion principle, John Riordan (mathematician), László Lovász, Martin Grötschel, Mathematical problem, Method of distinguished element, Natural number, Partition of a set, Pólya enumeration theorem, Penguin Books, Permutation, Recurrence relation, Richard P. Stanley, Ronald Graham, Sieve theory, Symbolic method (combinatorics), Tree (graph theory), Twelvefold way.
Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
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Algebraic enumeration
Algebraic enumeration is a subfield of enumeration that deals with finding exact formulas for the number of combinatorial objects of a given type, rather than estimating this number asymptotically.
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Anders Björner
Anders Björner (born 17 December 1947) received his Ph.D. from Stockholm University in 1979, under Bernt Lindström.
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Asymptotic analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.
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Burnside's lemma
Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma or the orbit-counting theorem, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Catalan number
In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.
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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Combination
In mathematics, a combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.
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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.
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Combinatorial game theory
Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information.
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Combinatorial principles
In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used.
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Combinatorial species
In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Doron Zeilberger
Doron Zeilberger (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics.
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Encyclopædia Britannica Eleventh Edition
The Encyclopædia Britannica Eleventh Edition (1910–11) is a 29-volume reference work, an edition of the Encyclopædia Britannica.
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Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Inclusion–exclusion principle
In combinatorics (combinatorial 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 where A and B are two finite sets and |S| indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite).
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John Riordan (mathematician)
John Francis Riordan (April 22, 1903 – August 27, 1988) was an American mathematician and the author of major early works in combinatorics, particularly Introduction to Combinatorial Analysis and Combinatorial Identities.
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László Lovász
László Lovász (born March 9, 1948) is a Hungarian mathematician, best known for his work in combinatorics, for which he was awarded the Wolf Prize and the Knuth Prize in 1999, and the Kyoto Prize in 2010.
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Martin Grötschel
Martin Grötschel (born 10 September 1948) is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research.
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Mathematical problem
A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics.
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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.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Partition of a set
In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.
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Pólya enumeration theorem
The Pólya enumeration theorem, also known as the Redfield–Pólya theorem, is a theorem in combinatorics that both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set.
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Penguin Books
Penguin Books is a British publishing house.
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Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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Richard P. Stanley
Richard Peter Stanley (born June 23, 1944 in New York City, New York) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts.
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Ronald Graham
Ronald Lewis "Ron" Graham (born October 31, 1935) is an American mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years".
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Sieve theory
Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers.
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Symbolic method (combinatorics)
In combinatorics, especially in analytic combinatorics, the symbolic method is a technique for counting combinatorial objects.
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Tree (graph theory)
In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.
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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 a set or of a number.
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Combinatorial enumeration, Enumerative Combinatorics.
References
[1] https://en.wikipedia.org/wiki/Enumerative_combinatorics
