Strong properties in partially ordered sets I

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.

Partially Ordered Sets

For example, thus far, I had the fortune to work intimately with nine (9) undergraduate students on research questions in the areas of computational algebra and algebraic geometry. I am directing two master’s students in their research for their theses at Sam Houston State University. All of these undergraduate students have enrolled in graduate programs around the country. Three have finished ...

Continuity in Partially Ordered Sets

Broadcasting in Partially Ordered Sets

Let be a partial order on a countable set V such that there exists a minimum element a ∈ V and {u ∈ V : u v} is finite for each v ∈ V . An item of information is to be broadcast to the elements of V according to the policy in the following sense: a is initially informed and broadcasting to v 6= a begins as soon as all elements u ≺ v are informed; the time required to broadcast the information i...

Properties of Mutual Rank Probabilities in Partially Ordered Sets

Karel De Loof1, Bernard De Baets2 and Hans De Meyer1 1Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium, (karel.deloof{hans.demeyer}@ugent.be) 2Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium, ([email protected]) Multicriteria Ordering and Ranking...