Some quotients of chain products are symmetric chain orders (Q456302)

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