Permutations Various ways to define a permutation Counting and listing all permutations Counting and listing all permutations: Johnson-Trotter Transpositions A Shuttle Puzzle Groups of Permutations Permutations as a Product of Transpositions Group multiplication of permutations Product of permutations Recombining Permutations Product of Permutations The applet below serves a demonstration for the product of permutations. It displays two permutations, say f and g, of numbers 1, 2, ..., N in a circular arrangement and their product fg below. Recollect that, for 1 ≤ k ≤ N,   (fg)(k) = g(f(k)), so that the left permutation is carried out first. The elements of the two permutations are clickable: clicking on two elements in a sequence in either of the permutations multiplies that permutation by a transposition of the two elements. This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet. Buy this applet Copyright © 1996-2008 Alexander Bogomolny

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