provide the notation and terminology for this paper. 1. POSET RETRACTS One can prove the following propositions: (1) For all binary relations a, b holds a · b = a b. (2) Let X be a set, L be a non empty relational structure, S be a non empty relational substruc-ture of L, f , g be functions from X into the carrier of S, and f , g be functions from X into the carrier of L. If f = f and g = g and...

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbo...

We study some poset structures on the set of all compositions. In the first case, the covering relation consists of inserting a part of size one to the left or to the right, or increasing the size of some part by one. The resulting poset N was studied by the author in [5] in relation to non-commutative term orders, and then in [6], where some results about generating functions for standard path...

We study the set S nc(p, q) of annular non-crossing permutations of type B, and we introduce a corresponding set NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We prove that the natural bijection between S nc(p, q) and NC (p, q) is a poset isomorphism, where the partial order on S nc(p, q) is induced from the hyperoctahedral group Bp+q, while NC ...

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

Let S be a signed poset in the sense of Reiner [4]. Fischer [2] defines the homology of S, in terms of a partial ordering P(S) associated to S, to be the homology of a certain subcomplex of the chain complex of P(S). In this paper we show that if P(S) is Cohen-Macaulay and S has rank n, then the homology of S vanishes for degrees outside the interval [n/2, n].

We consider generalizations of Schützenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weight...

For a closure space (P,φ) with φ(∅) = ∅, the closures of open subsets of P , called the regular closed subsets, form an ortholattice Reg(P,φ), extending the poset Clop(P,φ) of all clopen subsets. If (P,φ) is a finite convex geometry, then Reg(P, φ) is pseudocomplemented. The Dedekind-MacNeille completion of the poset of regions of any central hyperplane arrangement can be obtained in this way, ...

Results of R. Stanley and M. Masuda completely characterize the hvectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vectors. We also present new methods for constructing poset balls with specific h-...