Some Quotients of Chain Products are Symmetric Chain Orders

Canfield and Mason have conjectured that for all subgroups G of the automorphism group of the Boolean lattice Bn (which can be regarded as the symmetric group Sn) the quotient order Bn/G is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, Bn/G is an SCO whenever G is generated by powers of disjoint cycles. In addition, the Boolean lattice Bn can be replaced by any product of finite chains. The symmetric chain decompositions of Greene and Kleitman provide the basis for partitions of