Bill  Pletsch
E_mail: bpletsch@twi.cc.nm.us

Title: The Generation of Polya Polynomials and Some Experiments using
Macsyma

A theorem by George Polya can be used to determine the number of
double cosets HgK in a group G that are generated by subgroups H and
K. In order to apply the theory, the cycle polynomial of each group
must be computed.  This can be an extremely cumbersome process.  In
this paper, it will be shown how Polya polynomials of two classes of
groups, the Young group and the first order wreath product group, can
be generated by the CAS Macsyma.  In addition, via the vehicle of the
computer experiment, instances of great simpification have been
discovered and will be presented.