Every countable poset is embeddable in the poset of unsolvable terms

Every Poset Has a Central Element

It is proved that there exists a constant 6, f > 6 > 0, such that in every finite partially ordered set there is an element such that the fraction of order ideals containing that element is between 6 and 1 -6. It is shown that 6 can be taken to be at least (3-log, 5)/4~0.17. This settles a question asked independently by Colburn and Rival, and Rosenthal. The result implies that the information-...

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...

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 poset on connected graphs is Sperner

The poset of bipartitions

Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with respect to this partial order, the bipartitional relations on a set of size [Formula: see text] for...