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Let S be a finite set. A permutation ƒ of S is a one to one mapping from S onto S, i.e. In other words ƒ:x (x) for ƒ(x), ∀ x S; where (x) for ƒ(x) is called the image of x S under ƒ. Fixed or moved element Fixed: An element x S is said to be fixed if (x) ƒ = x, ∀ x S. Moved: An element x S is said to be moved by ƒ if it is not fixed by ƒ. Identity Permutation: The identity permutation is the permutation that fixes all the elements of S. It is generally, denoted by I and (x) I = x, ∀ x S. In other words, a permutation which takes every element of S onto itself is called the identity permutation. Illustration: If S = (1, 2, 3), then the identity permutation of S is
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