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.

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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 https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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What if applet does not run?

Permutations

• Various ways to define a permutation
• Counting and listing all permutations
• Johnson-Trotter Algorithm: Listing All Permutations

Transpositions

• The Futurama Theorem and Puzzle
• A Shuttle Puzzle

Groups of Permutations

• Group multiplication of permutations
• Permutations as a Product of Transpositions
• Product of permutations
• Recombining Permutations

Sliders

• Sam Loyd's Fifteen
• Lucky 7
• Happy 8
• Blithe 12
• Slider puzzles

Puzzles on graphs

Equation in Permutations

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