A special case of the Generalized Baues Conjecture states that the order complex of the Baues poset of an acyclic vector connguration A (the Baues complex of A) is homotopy equivalent to a sphere of dimension equal to the corank of A minus one. The Baues poset of A is the set of proper polyhedral subdivisions of A ordered by reenement. Recently, Santos has found a counterexample in corank 317 t...

Abstract Multipath cohomology is a theory for directed graphs, which defined using the path poset. The aim of this paper to investigate combinatorial properties posets and provide computational tools multipath cohomology. In particular, we develop acyclicity criteria computations groups oriented linear graphs. We further interpret poset as face simplicial complex, realisability problems.

In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of ...

in this paper, given a poset $(x,leq)$, we introduce some  drifts on a groupoid $(x,*)$ with respect to $(x,leq)$, and we obtain several properties of these drifts related to the notion of $bin(x)$. we discuss some connections between fuzzy subalgebras and upward drifts.

A graph Gs = (V,Es) is a sandwich for a pair of graph Gt = (V,Et) and G = (V,E) if Et ⊆ Es ⊆ E. Any poset, or partially ordered set, admits a unique graph representation which is directed and transitive. In this paper we introduce the notion of sandwich poset problems inspired by former sandwich problems on comparability graphs. In particular, we are interested in seriesparallel and interval po...

In this paper, given a poset $(X,leq)$, we introduce some  drifts on a groupoid $(X,*)$ with respect to $(X,leq)$, and we obtain several properties of these drifts related to the notion of $Bin(X)$. We discuss some connections between fuzzy subalgebras and upward drifts.

Notation and facts necessary to start with the formalization of continuous lattices according to [8] are introduced. The article contains among other things, the definition of directed and filtered subsets of a poset (see 1.1 in [8, p. 2]), the definition of nets on the poset (see 1.2 in [8, p. 2]), the definition of ideals and filters and the definition of maps preserving arbitrary and directe...

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, we formally define a useful data structure for content-based routing and event delivery. The poset (partially ordered set)-derived forest data structure is induced by the partial order created by the covering relation between event filters. Two extensions of the basic data structure are discussed: colored forests and the weakly merging forest. We give performance figures for the ...