A poset P = (X,≺) is a unit OC interval order if there exists a representation that assigns an open or closed real interval I(x) of unit length to each x ∈ P so that x ≺ y in P precisely when each point of I(x) is less than each point in I(y). In this paper we give a forbidden poset characterization of the class of unit OC interval orders and an efficient algorithm for recognizing the class. Th...

A distributed computation is usually modeled as a finite partially ordered set (poset) of events. Many operations on this poset require computing meets and joins of subsets of events. The lattice of normal cuts of a poset is the smallest lattice that embeds the poset such that all meets and joins are defined. In this paper, we propose new algorithms to construct or enumerate the lattice of norm...

Let n denote the lattice of partitions of an n-set, ordered by reenement. We show that for all large n there exist antichains in n whose size exceeds n 1=35 S (n; K n). Here S (n; K n) is the largest Stirling number of the second kind for xed n, which equals the largest rank within n. Some of the more complicated aspects of our previous proof of this result are avoided, and the variance of a ce...

We provide a combinatorial recipe for constructing all posets of height at most two which the corresponding type-A Lie poset algebra is contact. In case that such are connected, discrete Morse theory argument establishes posets' simplicial realizations contractible. It follows from cohomological result Coll and Gerstenhaber on semi-direct products contact algebras absolutely rigid.

Let G be a graph on [ n ] and J the binomial edge ideal of in polynomial ring S = K x 1 , … y . In this paper we investigate some topological properties poset associated to minimal primary decomposition We show that admits specific subposets which are contractible. This turn, provides interesting algebraic consequences. particular, characterize all graphs for depth / 4