  Homogeneous chain decompositions (HCDs) and noncrossing chain decompositions
(NcCDs) of a poset are studied here, the former having a close connection to
linear sequential dynamical systems while the latter generalizing the
well-known noncrossing partitions. There exists a unique HCD containing the
minimum number of chains for any poset and we show the number is not
necessarily Lipschitz. Making use of the unique HCD, we then identify a group
that contains an isomorphic copy of the automorphism group of the poset.
Finally, we prove some upper bounds for the minimum number of chains contained
in an NcCD. In particular, the number of chains in the unique HCD provides an
upper bound.
