  In this paper we analyze Garden-of-Eden (GoE) states and fixed points of
monotone, sequential dynamical systems (SDS). For any monotone SDS and fixed
update schedule, we identify a particular set of states, each state being
either a GoE state or reaching a fixed point, while both determining if a state
is a GoE state and finding out all fixed points are generally hard. As a
result, we show that the maximum size of their limit cycles is strictly less
than ${n\choose \lfloor n/2 \rfloor}$. We connect these results to the
Knaster-Tarski theorem and the LYM inequality. Finally, we establish that there
exist monotone, parallel dynamical systems (PDS) that cannot be expressed as
monotone SDS, despite the fact that the converse is always true.
