Some Quotients of the Boolean Lattice are Symmetric Chain Orders
Combinatorics
2011-08-29 v2
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.
Keywords
Cite
@article{arxiv.1107.1098,
title = {Some Quotients of the Boolean Lattice are Symmetric Chain Orders},
author = {Dwight Duffus and Jeremy McKibben-Sanders and Kyle Thayer},
journal= {arXiv preprint arXiv:1107.1098},
year = {2011}
}
Comments
The 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