In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these notions we will find three equivalent definitions, that will be shown to be equivalent. We start by defining partitions of a poset in terms of fibres of some su...

In this paper, concepts of strongly way below relations, completely precontinuous posets, coprimes and Heyting posets are introduced. The main results are: (1) The strongly way below relations of completely precontinuous posets have the interpolation property; (2) A poset P is a completely precontinuous poset iff its normal completion is a completely distributive lattice; (3) An ω-chain complet...

This paper continues a recent resurgence of interest in combinatorial properties of a poset that are associated with graph properties of its cover graph and order diagram. The following two theorems appearing in a 1977 paper of Trotter and Moore have played important roles in motivating this more modern research: (1) The dimension of a poset is at most 3 when its cover graph is at tree; (2) The...

We completely characterize the factorial functions of Eulerian binomial posets. The factorial function B(n) either coincides with n!, the factorial function of the infinite Boolean algebra, or 2n−1, the factorial function of the infinite butterfly poset. We also classify the factorial functions for Eulerian Sheffer posets. An Eulerian Sheffer poset with binomial factorial function B(n) = n! has...

Given an a$ne projection :PPQ of convex polytopes, let (P, ) be the re"nement poset of proper polyhedral subdivisions of Q which are induced by , in the sense of Billera and Sturmfels. Let (P, ) be the spherical subposet of -coherent subdivisions. It is proved here that the inclusion of the latter poset into the former induces injections in homology and homotopy. In particular, the poset (P, ) ...

In order to evaluate the creditworthiness of various countries, a learning model is induced from the 1998 S&P country risk ratings, using the 1998 values of nine economic and three political indicators. This learning model allows the construction of a partially ordered set describing the relative superiority of countries on the basis of their creditworthiness, and it is shown that the Condorcet...

A graph G s = (V , E s) is a sandwich for a pair of graphs G t = (V , E t) and G = (V , E) if E t ⊆ E s ⊆ E. A sandwich problem asks for the existence of a sandwich graph having an expected property. In a seminal paper, Golumbic et al. [Graph sandwich problems, J. Algorithms 19 (1995) 449–473] present many results on sub-families of perfect graphs. We are especially interested in comparability ...

We consider the poset of all posets on n elements where the partial order is that of inclusion of comparabilities. We discuss some properties of this poset concerning its height, width, jump number and dimension. We also give algorithms to construct some maximal chains in this poset which have special properties for these parameters.

Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voro...

In this paper we describe a novel a procedure to build a linear order from an arbitrary poset which (i) preserves the original ordering and (ii) allows to extend monotonic and antitonic mappings defined over the original poset to monotonic and antitonic mappings over the new linear poset.