We introduce a new type of dcpo-completion of posets, called D-completion. For any poset P , the D-completion exists, and P and its Dcompletion have the isomorphic Scott closed set lattices. This completion is idempotent. A poset P is continuous (algebraic) if and only if its D-completion is continuous(algebraic). Using the D-completion, we construct the local dcpocompletion of posets, that rev...

The jeu de taquin process produced a standard Young tableau from a skew standard Young tableau by shifting its entries to the northwest. We generalize this process to posets: certain partial numberings of any poset are shifted upward. A poset is said to have the jeu de taquin property if the numberings resulting from this process do not depend upon certain choices made during the process. Young...

Whereas the Dedekind-MacNeille completion D(P ) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P )∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is joinirreducible). In this paper we study lattices which a...

Denote by G and D, respectively, the the homomorphism poset of the finite undirected and directed graphs, respectively. A maximal antichain A in a poset P splits if A has a partition (B, C) such that for each p ∈ P either b ≤P p for some b ∈ B or p ≤p c for some c ∈ C. We construct both splitting and non-splitting infinite maximal antichains in G and in D. A point y ∈ P is a cut point in a pose...

In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...

Let K be a field and P partially ordered set (poset). FI(P,K) I(P,K) the finitary incidence algebra space of over K, respectively, let D(P,K)=FI(P,K)⊕I(P,K) idealization FI(P,K)-bimodule I(P,K). In first part this paper, we show that D(P,K) has an anti-automorphism (involution) if only (involution). We also present characterization anti-automorphisms involutions on D(P,K). second part, obtain c...

There are two related poset structures, the higher Stasheff-Tamari orders, on the set of all triangulations of the cyclic d polytope with n vertices. In this paper it is shown that both of them have the homotopy type of a sphere of dimension n d 3. Moreover, we resolve positively a new special case of the Generalized Baues Problem: The Baues poset of all polytopal decompositions of a cyclic pol...

Joret, Micek, Milans, Trotter, Walczak, and Wang recently asked if there exists a constant d such that if P is a poset with cover graph of P of pathwidth at most 2, then dim(P ) ≤ d. We answer this question in the affirmative. We also show that if P is a poset containing the standard example S5 as a subposet, then the cover graph of P has treewidth at least 3.

In every dense poset P every maximal antichain S may be partitioned into disjoint subsets S1 and S2 , such that the union of the upset of S1 with the downset of S2 yields the entire poset: U(S1) [ D(S2) = P . To nd a similar splitting of maximal antichains in posets is NP{hard in general.

Let D = (V (D), A(D)) be a digraph. The competition graph of D, is the graph with vertex set V (D) and edge set {uv ∈ `V (D) 2 ́ : ∃w ∈ V (D),−→ uw,−→ vw ∈ A(D)}. The double competition graph of D, is the graph with vertex set V (D) and edge set {uv ∈ `V (D) 2 ́ : ∃w1, w2 ∈ V (D),−−→ uw1,−−→ vw1,−−→ w2u,−−→ w2v ∈ A(D)}. A poset of dimension at most two is a digraph whose vertices are some points ...