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Permutation and Permutation group

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Permutation and Permutation group

Permutation vs. Permutation group

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. In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself).

Similarities between Permutation and Permutation group

Permutation and Permutation group have 21 things in common (in Unionpedia): Associative property, Augustin-Louis Cauchy, Évariste Galois, Bijection, Cardinality, Cayley's theorem, Combinatorics, Ernő Rubik, Factorial, Finite set, Function composition, Group (mathematics), Group action, Identity function, Inverse function, Isomorphism, Joseph-Louis Lagrange, Mathematics, Permutation, Set (mathematics), Symmetric group.

Associative property

In mathematics, the associative property is a property of some binary operations.

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Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

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Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.

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Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

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Cardinality

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

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Cayley's theorem

In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. This can be understood as an example of the group action of G on the elements of G. A permutation of a set G is any bijective function taking G onto G; and the set of all such functions forms a group under function composition, called the symmetric group on G, and written as Sym(G).

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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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Ernő Rubik

Ernő Rubik (born 13 July 1944) is a Hungarian inventor, architect and professor of architecture.

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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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Finite set

In mathematics, a finite set is a set that has a finite number of elements.

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Function composition

In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

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Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

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Identity function

Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.

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Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

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Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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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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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

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The list above answers the following questions

Permutation and Permutation group Comparison

Permutation has 113 relations, while Permutation group has 39. As they have in common 21, the Jaccard index is 13.82% = 21 / (113 + 39).

References

This article shows the relationship between Permutation and Permutation group. To access each article from which the information was extracted, please visit:

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