Symmetric chain decomposition of necklace posets

Vivek Dhand

Published 2011-04-21, updated 2012-12-18Version 3

A finite ranked poset is called a symmetric chain order if it can be written as a disjoint union of rank-symmetric, saturated chains. If $P$ is any symmetric chain order, we prove that $P^n/\mathbb{Z}_n$ is also a symmetric chain order, where $\mathbb{Z}_n$ acts on $P^n$ by cyclic permutation of the factors.