In 2001, S. Bulman-Fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $A_{S}$ over a monoid $S$ that can be described by means of when the functor $A_{S} otimes -$ preserves pullbacks. In this paper, we extend these results to $S$-posets and present equivalent descriptions of weakly kernel p...

This article extends a paper of Abraham and Bonnet which generalised the famous Hausdorff characterisation of the class of scattered linear orders. Abraham and Bonnet gave a poset hierarchy that characterised the class of scattered posets which do not have infinite antichains (abbreviated FAC for finite antichain condition). An antichain here is taken in the sense of incomparability. We define ...

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.

We give a new order-theoretic characterization of a complete Heyting and co-Heyting algebra C. This result provides an unexpected relationship with the field of Nash equilibria, being based on the so-called Veinott ordering relation on subcomplete sublattices of C, which is crucially used in Topkis’ theorem for studying the order-theoretic stucture of Nash equilibria of supermodular games. Intr...

In this paper we discuss the Bruhat order of the symmetric group. We give two criteria for comparing elements in this poset and show that the poset is Eulerian. We also discuss the notion of shellability and EL-shellability, and use this concept to show that the order complex associated to the Bruhat order triangulates a sphere.

A simplicial poset P (also called a boolean poset and a poset of boolean type) is a finite poset with a smallest element 0̂ such that every interval [0̂, y] for y ∈ P is a boolean algebra, i.e., [0̂, y] is isomorphic to the set of all subsets of a finite set, ordered by inclusion. The set of all faces of a (finite) simplicial complex with empty set added forms a simplicial poset ordered by inclusi...