Partitions into Even and Odd Block Size and Some Unusual Characters of the Symmetric Groups

For each n and k, let II sup (~(i,k)) sub n denote the poset of all partitions of n having every block size congruent to i mod k. Attach to II sup (~(i,k)) sub n a unique maximal or minimal element if it does not already have one, and denote the resulting poset II sup (i,k) sub n. Results of Bjorner, Sagan and Wachs show that II sup (o,k) sub n and II sup (l,k) sub n are lexicographically shellable, and hence Cohen-Macaulay.