The Spider Poset is
نویسنده
چکیده
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 n th cartesian power of the spider poset Q(k; l) is a Macaulay poset for any k 0 and l 1. In combination with our recent results 2] this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices, whose Hasse diagrams are trees.
منابع مشابه
The Spider Poset Is Macaulay
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 the spider poset Q(k, l) is a Macaulay poset for any k ≥ 0 and l ≥ 1. In combination with our recent results [2] this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices,...
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