Some cardinal characteristics of ordered sets

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Some Representation Theorems for Partially Ordered Sets

Some sharply transitive partially ordered sets

A partially ordered set (X, is called sharply transitive if its automorphism group is sharply transitive on X, that is, it is transitive and the stabilizer of every element is triviaL It is shown that every free group is the automorphism group of a sharply transitive partially ordered set. It is also shown that there exists a sharply transitive partially ordered set (-,Y, :::;) having some maxi...

Perfect Codes on Some Ordered Sets

Using the concept of codes on ordered sets introduced by Brualdi, Graves and Lawrence, we consider perfect codes on the ordinal sum of two ordered sets, the standard ordered sets and the disjoint sum of two chains. In the classical coding theory all perfect codes are completely described in terms of parameters (cf. [2, 3]). They are mathematically interesting structures. Brualdi et al. [1] rece...

Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the termin...