Symmetric chain decomposition of necklace posets (Q426785)

Summary: 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 \(\mathcal{P}\) is any symmetric chain order, we prove that \(\mathcal{P}^n/\mathbb{Z}_n\) is also a symmetric chain order, where \(\mathbb{Z}_n\) acts on \(\mathcal{P}^n\) by cyclic permutation of the factors.