Totally unordered subsets of a partially well ordered set

Sampling of Multiple Variables Based on Partially Ordered Set Theory

We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation...

Partitions of a Finite Partially Ordered Set

In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these notions we will find three equivalent definitions, that will be shown to be equivalent. We start by defining partitions of a poset in terms of fibres of some su...

Partially Well-Ordered Closed Sets of Permutations

It is known that the \pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally de ned subsets of permutations are partially well-ordered, in which case they have a strong nite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as...

Mining Induced and Embedded Subtrees in Ordered, Unordered, and Partially-Ordered Trees

Many data mining problems can be represented with nonlinear data structures like trees. In this paper, we introduce a scalable algorithm to mine partially-ordered trees. Our algorithm, POTMiner, is able to identify both induced and embedded subtrees and, as special cases, it can handle both completely ordered and completely unordered trees (i.e. the particular situations existing algorithms add...

Semi-t-operators on a finite totally ordered set