This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to prov...

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...

This paper introduces two new decomposition techniques which are related to the classical notion of shellability of simplicial complexes, and uses the existence of these decompositions to deduce certain numerical properties for an associated enumerative invariant. First, we introduce the notion of M-shellability, which is a generalization to pure posets of the property of shellability of simpli...

We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting 0,∞ ,≤ that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment results and results concerning ladder variables and point processes. We concentrate mostly on discrete posets, par...

We prove that the posets of connected components of intersections of toric and elliptic arrangements defined by root systems are EL-shellable and we compute their homotopy type. Our method rests on Bibby’s description of such posets by means of “labeled partitions”: after giving an EL-labeling and counting homology chains for general posets of labeled partitions, we obtain the stated results by...

In this paper we study finite Eulerian posets which are binomial or Sheffer. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows: (1) We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets; (2...

Abstract The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension relative pseudocomplementation for not necessarily distributive lattices. typical example such is the non-modular N 5 . aim this paper to extend sectional from lattices posets. At first we show that class forms variety which can be described by two simple identities. This has nice ...