  In 2002 R. Suter identified a dihedral symmetry on certain order ideals in
Young's lattice and gave a combinatorial action on the partitions in these
order ideals. Viewing this result geometrically, the order ideals can be seen
to be seen to be in bijection with the alcoves in a 2-fold dilation in the
geometric realization of the affine symmetric group. By considering the m-fold
dilation we observe a larger set of order ideals in the k-bounded partition
lattice that was considered by L. Lapointe, A. Lascoux, and J. Morse in the
study of k-Schur functions. We identify the order ideal and the cyclic action
on it explicitly in a geometric and combinatorial form.
