We present an equivariant bijection between two actions—promotion and rowmotion—on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and certain cases of recent work of D. Armstrong, C. Stump, and H. Thomas on noncrossing and nonnesting partitions. We apply this bijection to sever...

This paper is devoted to the study of products of classes of right $S$-posets possessing one of the flatness properties and preservation of such properties under products. Specifically, we characterize a pomonoid $S$ over which its nonempty products as right $S$-posets satisfy some known flatness properties. Generalizing this results, we investigate products of right $S$-posets satisfying Condi...

Whereas the Dedekind-MacNeille completion D(P ) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P )∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is joinirreducible). In this paper we study lattices which a...

In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. In this article first of all we describe po-flatness propertie...

In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...

For a number of locally finitely presentable categories K we describe the codensity monad full embedding all objects into K. We introduce concept D-ultrafilter on an object, where D is “nice” cogenerator prove that assigns to every object representing D-ultrafilters it. Our result covers e.g. sets, vector spaces, posets, semilattices, graphs and M-sets for finite commutative monoids M.

A class of ranked posets {(D h, )} has been recently defined in order to analyse, from a combinatorial viewpoint, particular systems of real homogeneous inequalities between monomials. In the present paper we focus on the posets D 2 , which are related to systems of the form {xaxb ∗abcd xcxd : 0 ≤ a, b, c, d ≤ k, ∗abcd ∈ {<, >}, 0 < x0 < x1 < ... < xk}. As a consequence of the general theory, t...

Conditional probability plays a basic role in the classical probability theory. Some of the most important areas of the theory such as martingales, stochastic processes rely heavily of this concept. Conditional probabilities on a classical measurable space are studied in several different ways, but result in equivalent theories. The classical probability theory does not describe the causality m...

Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of T0 spaces instead of restricting to posets. In this paper, we respond to this calling by proving a topological parallel of a 2005 result due to B. Zhao and D. Zhao, i.e., an order-theoretic characterisation of those posets for which the lim-inf con...