The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

In this paper, we investigate po-purity using finitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly finitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right con...

Given an affine surjection of polytopes : P ! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes : C(n; ...

We prove that if a nite lattice L has order dimension at most d, then the homology of the order complex of its proper part L vanishes in dimensions d ? 1 and higher. In case L can be embedded as a join-sublattice in N d then L actually has the homotopy type of a simplicial complex with d vertices. 1. Introduction. The order dimension OrderDim(P) of a nite partially ordered set (poset for short)...

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...

(a) P is a nonempty set; (b) ≤ is a partial ordering of P; i.e., ≤ is transitive, reflexive relation in P (and so p ≤ q ∧ q ≤ p ∧ p 6= q is not forbidden); (c) for all p ∈ P, p ≤ 1. (1 need not be the only such maximum element.) We shall often write P for 〈P,≤,1〉. Let P be a poset. If p is an element of P, then an extension of p is a q ∈ P such that q ≤ p. Two elements of P are compatible if th...

A coloured poset is a poset with a unique maximal element that is equipped with a sheaf of modules. In this paper we initiate the study of a bundle theory for coloured posets, producing for a certain class of base posets a LeraySerre type spectral sequence. We then show how this theory finds application in Khovanov homology by producing a new spectral sequence converging to the Khovanov homolog...

Given a partially ordered set P = (X,P), a function F which assigns to each x E X a set F(x) so that x ~<y in P if and only if F(x)C F(y) is called an inclusion representation. Every poser has such a representation, so it is natural to consider restrictions on the nature of the images of the function F. In this paper, we consider inclusion representations assigning to each x E X a sphere in ~d,...

Consider points (x 1 ; y 1) and (x 2 ; y 2) in < 2. We say (x 1 ; y 1) is dominated by (x 2 ; y 2) if x 1 < x 2 and y 1 < y 2. If (x 1 ; y 1) is dominated by (x 2 ; y 2), then we write (x 1 ; y 1) < D (x 2 ; y 2). For any nite subset P < 2 , the partially ordered set (P; D) is called the dominance poset. In this paper we present two distributed algorithms to compute the maximal points of a domi...