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Exploring Cycle Notation

James Hamblin (Shippensburg Univ.)

These two Flash applets allow students to work through simple exercises involving permutations and "cycle notation" for the teaching of elementary concepts in Group Theory or Discrete Mathematics.  The applets are entirely browser-based and require only a browser with the (free) Flash Player plugin, v9 or higher.

Clicking a link (or thumbnail) below opens a page with instructions, suggestions, and the applet itself in a separate window.

Cycle Notation - This applet allows a user to input a one-to-one and onto function and generate the cycle notation. It can also generate a random function and the corresponding cycle notation.

Cycle Notation Generator

Cycle Composer - This applet allows the user to see how the product operation works in Sym(4), the symmetric group on 4 symbols.

 Composition of Permutations 
Note: The Flash source code along with other Flash-based teaching and learning tools can be found on the author's website,

James Hamblin (Shippensburg Univ.), "Exploring Cycle Notation," Convergence (February 2010), DOI:10.4169/loci002858