Some Sufficient Conditions for Finding a Nesting of the Normalized Matching Posets of Rank 3

Yu-Lun Chang, Wei-Tian Li

Given a graded poset $P$, consider a chain decomposition $\mathcal{C}$ of $P$. If $|C_1|\le |C_2|$ implies that the set of the ranks of elements in $C_1$ is a subset of the ranks o…