In this article we characterize all those sequences of cardinals
of length which are cardinal sequences of some (locally)
compact scattered
space (or, equivalently, a superatomic boolean algebra).
This extends the similar results from [LG] for such sequences
of countable length.
For ordinals between and we can only
give a sufficient condition for a sequence of that length to be a
cardinal sequence of a compact scattered space.
This condition is, arguably, the most one can expect in
ZFC. In any case, ours is a significant extension of the
sufficient conditions given in [M] and [B].