A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper...

In this paper, we focus on a “local property” of permutations: value-peak. A permutation σ has a value-peak σ(i) if σ(i − 1) < σ(i) > σ(i + 1) for some i ∈ [2, n − 1]. Define V P (σ) as the set of value-peaks of the permutation σ. For any S ⊆ [3, n], define V Pn(S) such that V P (σ) = S. Let Pn = {S | V Pn(S) 6= ∅}. we make the set Pn into a poset Pn by defining S T if S ⊆ T as sets. We prove t...

A zircon is a poset in which every principal order ideal is finite and equipped with a so-called special matching. We prove that the subposet induced by the fixed points of any automorphism of a zircon is itself a zircon. This provides a natural context in which to view recent results on Bruhat orders on twisted involutions in Coxeter groups. 1. Background and results Let P be a partially order...

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 ...

Contents Poset Topology: Tools and Applications 1 Introduction 3 Lecture 1. Basic definitions, results, and examples 5 1.1. Order complexes and face posets 5 1.2. The Möbius function 9 1.3. Hyperplane and subspace arrangements 11 1.4. Some connections with graphs, groups and lattices 16 1.5. Poset homology and cohomology 17 1.6. Top cohomology of the partition lattice 19 Lecture 2. Group action...

From the work of Simmons about nuclei in frames it follows that a topological space X is scattered if and only if each congruence Θ on the frame of open sets is induced by a unique subspace A so that Θ = {(U, V ) |U ∩A = V ∩A}, and that the same holds without the uniqueness requirement iff X is weakly scattered (corrupt). We prove a seemingly similar but substantially different result about qua...

We investigate the combinatorics and the topology of the poset of strata of a Schubert like stratification on the Grassmannian of hermitian lagrangian spaces in Cn ⊕ Cn. We prove that this poset is a modular complemented lattice, we compute its Möbius function and we investigate the combinatorics and the topology of its order intervals.

The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even ...

The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this  structure.