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...

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 po...

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, ) ...

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 study different problems of enumeration of standard paths in the poset of compositions of integers. We show that several problems similar to those considered in the poset of partitions of integers become simpler in this context. We give explicit formulas for generating functions of standard paths in this poset and interesting subposets, and a closed formula for the number of standard paths e...

The standard poset transit function of a poset P is a function TP that assigns to a pair of comparable elements the interval between them, while TP (x, y) = {x, y} for a pair x, y of incomparable elements. Posets in which the standard poset transit function coincides with the shortest-path transit function of its cover-incomparability graph are characterized in three ways, in particular with fo...

Term occurrences of any clause C are determined by their positions. The set of all term partitions defined on subsets of term occurrences of C form a partially ordered set. This poset is isomorphic to the set of all generalizations of C. The structure of this poset can be inferred from the term occurrences in C alone. We can apply these constructions in this poset in machine learning.