symmetric chain decomposition

Let $P$ be a finite ranked poset with rank numbers $r_{1}, \dots, r_{l} \geq 1$ . A symmetric chain decomposition of $P$ is a collection of chains $C_{1}, C_{2}, \dots, C_{n} \subseteq P$ such that

$⋃_{i} C_{i} = P$ (ie. that it covers $P$ )
For all $C_{i} = c_{0} < c_{1} < \dots < c_{s}$ , $ρ (c_{s}) = l - ρ (c_{0})$ (ie. it is symmetric about the middle)

necessary conditions for scd