Permutations

Abstract

Permutations A permutation of {1, …, n } is a 1-1, onto mapping of the set to itself. Most books initially use a bulky notation to describe a permutation: The numbers 1..n are put on one row and the images of these elements under the permutation are put below. Thus       3 3 1 2 2 1 describes the permutation which sends 1 ! 2, 2 ! 1, 3 ! 3. This is quickly abandoned in favor of a 1 line "cycle notation" where the same permutation would be denoted (1 2). Groups32 uses cycle notation. It may be of interest for you to know that Groups32 internally stores permutations in the bulky notation and converts them, for input and output, to the cycle notation.