We consider the follow poset merging problem: Let X and Y be two subsets of a partially ordered set S. Given complete information about the ordering within both X and Y , how many comparisons are needed to determine the order on X ∪ Y ? This problem is a natural generalization of the list merging problem. While searching in partially ordered sets and sorting partially ordered sets have been con...

An occurrence of a consecutive permutation pattern p in a permutation π is a segment of consecutive letters of π whose values appear in the same order of size as the letters in p. The set of all permutations forms a poset with respect to such pattern containment. We compute the Möbius function of intervals in this poset. For most intervals our results give an immediate answer to the question. I...

The dimension of a poset X is the smallest positive integer t for which there exists an embedding of X in the cartesian product of t chains. R. P. Dilworth proved that the dimension of a distributive lattice v L = 2_ is the width of X. In this paper we derive an analogous result for embedding distributive lattices in the cartesian product of chains of bounded length. We prove that for each k > ...

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 some properties of weak regular injectivity for $S$-posets‎, ‎where $S$ is a pomonoid‎, ‎are studied‎. ‎The behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎Also‎, ‎some‎ ‎characterizations of pomonoids over which all $S$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎Further‎, ‎we‎ ‎giv...

The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset, describing structural, characterizing, and enumerative properties.

This work is devoted to give a charcaterization of a pomonoid $S$ such that all cyclic $S$-posets are regular injective.