The Spider Poset Is Macaulay

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,...

The Spider Poset is

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, whos...

On the Möbius function of a lower Eulerian Cohen–Macaulay poset

A certain inequality is shown to hold for the values of the Möbius function of the poset obtained by attaching a maximum element to a lower Eulerian Cohen– Macaulay poset. In two important special cases, this inequality provides partial results supporting Stanley’s nonnegativity conjecture for the toric h-vector of a lower Eulerian Cohen–Macaulay meet-semilattice and Adin’s nonnegativity conjec...

The poset on connected graphs is Sperner

The Essential Ideal Is a Cohen–macaulay Module

Let G be a finite p-group which does not contain a rank two elementary abelian p-group as a direct factor. Then the ideal of essential classes in the mod-p cohomology ring of G is a Cohen–Macaulay module whose Krull dimension is the p-rank of the centre of G. This basically answers in the affirmative a question posed by J. F. Carlson (Question 5.4 in [7]).