  The (n,k)-arrangement graph A(n,k) is a graph with all the k-permutations of
an n-element set as vertices where two k-permutations are adjacent if they
agree in exactly k-1 positions. We introduce a cyclic decomposition for
k-permutations and show that this gives rise to a very fine equitable partition
of A(n,k). This equitable partition can be employed to compute the complete set
of eigenvalues (of the adjacency matrix) of A(n,k). Consequently, we determine
the eigenvalues of A(n,k) for small values of k. Finally, we show that any
eigenvalue of the Johnson graph J(n,k) is an eigenvalue of A(n,k) and that -k
is the smallest eigenvalue of A(n,k) with multiplicity O(n^k) for fixed k.
