  Despite a blossoming of research activity on racks and their homology for
over two decades, with a record of diverse applications to central parts of
contemporary mathematics, there are still very few examples of racks whose
homology has been fully calculated. In this paper, we compute the entire
integral homology of all permutation racks. Our method of choice involves
homotopical algebra, which was brought to bear on the homology of racks only
recently. For our main result, we establish a spectral sequence, which reduces
the problem to one in equivariant homology, and for which we show that it
always degenerates. The blueprint given in this paper demonstrates the high
potential for further exploitation of these techniques.
