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Permutation

Combinatorics and Graph Theory

A permutation is a bijection of a set onto itself, interpreted either as a new order of the members of a sequence or as the act of changing the linear order of an ordered set; the six permutations of the set {1, 2, 3} are an example of the first interpretation. The number of permutations of n distinct objects is n factorial, and the study of permutations of finite sets is an important topic in combinatorics and group theory, applied across computer science, quantum physics and biology. The collection of all permutations of a set forms a group, called the symmetric group of the set, under the operation of composing permutations. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Origin Year
1150 1
Earliest documented general counting rule per this source, in Indian mathematics circa 1150 AD; ad hoc permutation-like arrangements (Chinese I Ching hexagrams, Greek syllable counts, medieval Arabic cryptography) predate this and are less precisely datable as a general rule.
Connections

Associated With

Bijection, Concepts
Group (Abstract Algebra), Concepts

The permutations of a set, composed under the bijection operation, form the symmetric group on that set, so permutation is the concept the symmetric group's elements are made of.

Additional Source Permutation (Wikipedia)Lead section

In Branch

Source Permutation (Wikipedia)
Sources
1. Permutation (Wikipedia)
Wikimedia Foundation
  • Lead section
    a permutation is a bijection of a set onto itself
  • History section
    The rule to determine the number of permutations of n objects was known in Indian culture around 1150 AD.
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