TITLE: Counting Special Monomials

AUTHORS: Chris Monico and Mara D. Neusel
Department of Mathematics and Statistics, MS 1042, 
Texas Tech University, Lubbock, Texas 79409

ABSTRACT:
In this paper we study the number of orbits of special monomials of G 
acting by permutations on the polynomials in n variables. We give formulae 
for several crucial families of groups, for direct sums
of representations, as well as for vector invariants. In addition we give 
two algorithms for arbitrary permutation groups, one relying on the 
geometry of G acting on the underlying vector space, the other relying on 
the representation theory of the symmetric groups.