Semi-t-operators on a finite totally ordered set

Semi-t-operators on a finite totally ordered set

The Number of Convex Topologies on a Finite Totally Ordered Set

We give an algorithm to find the number Tcvx(n) of convex topologies on a totally ordered set X with n elements, and present these numbers for n ≤ 10. 2010 Mathematics Subject Classification: 54A10, 54F05, 06F30, 05A15.

The Imbedding Operators on a Partially Ordered Set

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...

On Sorting an Intransitive Total Ordered Set Using Semi-Heap

1 The problem of sorting an intransitive total ordered set, a generalization of regular sorting, is considered. This generalized sorting is based on the fact that there exists a special linear ordering for any intransitive total ordered set. A new data structure called semi-heap is proposed to construct an optimal (n logn) sorting algorithm. Finally, we propose a cost-optimal parallel algorithm...