  We consider random mappings on n = kr nodes with preimage sizes restricted to
a set of the form {0,k}, where k = k(r) is greater than 1. We prove that T, the
least common multiple of the cycle lengths, and B= the product of the cycle
lengths, are both asymptotically lognormal. The expected values of these random
variables are also also estimated and compared with numerical results. This
work is motivated, in part, by the use of these mappings as heuristic models
for polynomials of the form x^k + a over the integers modulo p with p congruent
to 1 mod k.
