A Recursion of the Symmetric Group's Polya Polynomial

Bill Pletsch
Central New Mexico Community College, Albuquerque, New Mexico, USA

The Polya polynomial of the symmetric group is a useful beast.  Its computation
is a bear.  A recursion developed by the author somewhat tames the beast.
When coupled with computer algebra a powerful data gathering tool is created.
The recursion, a sketch of its proof, and the link with computer algebra will
be discussed.  Finally, if there is time, some of the patterns discovered and
the results they reveal in the theory of double cosets, rearrangement
reactions, contingency tables, integer sequences, and stochastic matrices will
be discussed.