  We consider N=4 theories on ALE spaces of $A_{k-1}$ type. As is well known,
their partition functions coincide with $A_{k-1}$ affine characters. We show
that these partition functions are equal to the generating functions of some
peculiar classes of partitions which we introduce under the name 'orbifold
partitions'. These orbifold partitions turn out to be related to the
generalized Frobenius partitions introduced by G. E. Andrews some years ago. We
relate the orbifold partitions to the blended partitions and interpret
explicitly in terms of a free fermion system.
