On-line chain partitioning problem of on-line posets has been open for the past 20 years. The best known on-line algorithm uses 5 w −1 4 chains to cover poset of width w. Felsner [3] introduced a variant of this problem considering only up-growing posets, i.e. on-line posets in which each new point is maximal at the moment of its arrival. He presented an algorithm using (

We prove a theorem allowing us to find convex-ear decompositions for rankselected subposets of posets that are unions of Boolean sublattices in a coherent fashion. We then apply this theorem to geometric lattices and face posets of shellable complexes, obtaining new inequalities for their h-vectors. Finally, we use the latter decomposition to give a new interpretation to inequalities satisfied ...

We study differential posets, a family of partially ordered sets discovered by Richard Stanley. In the first half of this paper we present an introduction to poset theory as relevant to differential posets and theorems on the structure and combinatorial properties of differential posets, culminating in the explicit definition of a new differential poset. In the second half we focus on Young’s l...

In this paper we consider languages of labelled N -free posets over countable and scattered linear orderings. We prove that a language of such posets is series-rational if and only if it is recognizable by a finite depth-nilpotent algebra if and only if it is bounded-width and monadic second-order definable. This extends previous results on languages of labelled N -free finite and ω-posets and ...

A long-standing conjecture states that posets with the normalized matching property are nested chain orders. We verify this conjecture for posets of rank 2.

The queue number of a poset is the its cover graph when vertex order linear extension poset. Heath and Pemmaraju conjectured that every width w has at most w. conjecture been confirmed for posets $$w=2$$ planar with 0 1. In contrast, refused by family general (non-planar) $$w>2$$ . this paper, we study layouts two-dimensional posets. First, construct $$w > 2$$ $$2(w - 1)$$ , thereby disproving ...