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 ...

We present the smallest non-lattice orthomodular poset and show that it is unique up to isomorphism. Since not every Boolean orthomodular, we consider class of skew posets previously introduced by first third author under name “generalized posets”. this contains all study its subclass consisting horizontal sums posets. For purpose, introduce concept a compatibility relation so-called commutator...

The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite series-parallel posets P. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable,...