  We present several multi-variable generating functions for a new pattern
matching condition on the wreath product of the cyclic group and the symmetric
group. Our new pattern matching condition requires that the underlying
permutations match in the usual sense of pattern matching for the symmetric
group and that the corresponding sequence of signs match in the sense of words,
rather than the exact equality of signs which has been previously studied. We
produce the generating functions for the number of matches that occur in
elements of the wreath product for any pattern of length 2 by applying
appropriate homomorphisms from the ring of symmetric functions over an infinite
number of variables to simple symmetric function identities. We also provide
multi-variable generating functions for the distribution of non-overlapping
matches and for the number of elements of the wreath product which have exactly
2 matches which do not overlap for several patterns of length 2.
