: Mathématiques: symmetric group

mathematical analysis > combinatorics > permutation > symmetric group

algebra > combinatorics > permutation > symmetric group

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. In particular, the finite symmetric group ${\\displaystyle \\mathrm {S} _{n}}$ defined over a finite set of ${\\displaystyle n}$ symbols consists of the permutations that can be performed on the ${\\displaystyle n}$ symbols. Since there are ${\\displaystyle n!}$ ( ${\\displaystyle n}$ factorial) such permutation operations, the order (number of elements) of the symmetric group ${\\displaystyle \\mathrm {S} _{n}}$ is ${\\displaystyle n!}$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Symmetric_group)

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