If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs ...
Let Q(k, l) be a poset whose Hasse diagram is a regular spider with k+1 legs having the same length l (cf. Fig. 1). We show that for any n 1 the nth cartesian power of