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. (To emphasize this fact, (fg)(k) is often written as kfg.)

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.


What if applet does not run?

Permutations

  • Transpositions
  • Groups of Permutations
  • Sliders
  • Puzzles on graphs
  • Equation in Permutations

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