Permutation
In mathematics, the notion of
permutation relates to the act of
permuting, or rearranging, members of a set into a particular sequence or order. For example, there are six permutations of the set, namely, , , , , and. As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. The study of permutations of finite sets is a topic in the field of combinatorics. The number of permutations of
n distinct objects is
n factorial usually written as "
n!", which means the product of all positive integers less than or equal to
n. Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered, possibly only because one wants to ignore such orderings and needs to know how many configurations are thus identified. For similar reasons permutations arise in the study of sorting algorithms in computer science. In algebra and particularly in group theory, a permutation of a set
S is defined as a bijection from
S to itself.