Covering graphs of various types of finite partially ordered sets have been extensively studied since Ore in [2] asked for a characterization of such graphs in general. In this note we introduce a graph, called the m-chain graph of a poset, that reduces to the covering graph when m = 1. Since we will show how to construct the m-chain graph for m > 2 as the 2-chain graph of another poset, we are...

By the Central Element Theorem of Linial and Saks, it follows that for the problem of (generalised) sea.rching in posets, the information-theoretic lower bound of log N comparisons (where N is the number of order-ideals in the poset) is tight asymptotically. We observe that this implies that the problem of (generalised) sorting in posets has complexity 9( n . log N) (where n is the number of de...

Abstract We prove that it is consistent Club Stationary Reflection and the Special Aronszajn Tree Property simultaneously hold on $\omega _2$ , thereby contributing to study of tension between compactness incompactness in set theory. The poset which produces final model follows collapse an ineffable cardinal first with iteration club adding (with anticipation) second specializing trees. In part...

If p is a prime number, the poset of all nontrivial elementary abelian p -subgroups of a finite group plays an important role in both group theory and representation theory. It was studied by Quillen [9], who proved among many other things that it is homotopy equivalent to the poset of all nontrivial p -subgroups. In the case of a p -group P , one might believe that this poset has no interest s...

A partial order or poset   , P X   on a (finite) base set X determines the set   P  of linear extensions of P . The problem of computing, for a poset P , the cardinality of   P  is #P-complete. A set   1 2 , , , k P P P  of posets on X covers the set of linear orders that is the union of the   i P  . Given linear orders 1 2 , , , m L L L  on X , the Poset Cover problem is to de...

We study the computational problem of checking whether a quantified conjunctive query (a first-order sentence built using only conjunction as Boolean connective) is true in a finite poset (a reflexive, antisymmetric, and transitive directed graph). We prove that the problem is already NP-hard on a certain fixed poset, and investigate structural properties of posets yielding fixedparameter tract...

In an Appalachian Set Theory Workshop [3], Gitik presented some of the details of a simplified version of the poset from his original paper. The discussion there motivates the definition of the forcing by modifying a poset which requires a stronger large cardinal assumption which is sometimes called the long extender forcing. However, the discussion recorded in the Appalachian Set Theory (AST) ...

Spines T a tree on a signed ground set V = V− t V. Spine on T = directed and labeled tree S such that • the labels of the nodes of S form a partition of the signed ground set V, • at a node labeled by U = U− t U, the source label sets of the incoming arcs are subsets of distinct connected components of TrU−, and the sink label sets of the outgoing arcs are subsets of distinct connected componen...

in (golchin a. and rezaei p., subpullbacks and flatness properties of s-posets. comm. algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. in this article first of all we describe po-flatness propertie...

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.