Some Quotients of the Boolean Lattice are Symmetric Chain Orders

Abstract

R. Canfield has 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. The symmetric chain decompositions of Greene and Kleitman provide the basis for partitions of these quotients.

arXiv commentThe significant changes from the first version are: inclusion of Theorem 3 and Corollary 1, with the proof of the former in Section 5. Small corrections and rewordings have been done as well

Cited by in corpus (2)

• Symmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals
• Geometric Symmetric Chain Decompositions