  The symmetric group S_n acts on the skew polynomial ring A=k_{-1}[x_1,...,
x_n] as permutations. For subgroups G of S_n we consider properties of the ring
of invariants A^G. We show that A^G is always Artin-Schelter Gorenstein, and we
investigate when A^G is a "complete intersection", in a sense we define. We
obtain bounds on the degrees of the algebra generators. The properties of A^G
are compared with those in the classical case, k[x_1, ..., x_n]^G.
