Some Quotients of the Boolean Lattice are Symmetric Chain Orders

Details Some Quotients of the Boolean Lattice are Symmetric Chain Orders Some Quotients of the Boolean Lattice are Symmetric Chain Orders

2011-07-06

arxiv.org/abs/1107.1098v2

Mathematics

Combinatorics

The significant changes from the first version are: inclusion of Theorem 3 and Corollary 1, with the proof of the former in Se

Scientific paper

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.

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