A cancellation law for partially ordered sets and $T_0$ spaces

A Cancellation Law for Partially Ordered Sets and T0 Spaces

In this paper we prove a cancellation law in the category (1) of partially ordered sets and (2) of T0 spaces, the respective conditions on the common factor being that it have (1) an irreducible bottom element and (2) an irreducible bottom element in its specialization order.

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.

Majorization for partially ordered sets

We generalize the classical notion of majorization in Rn to a majorization order for functions defined on a partially ordered set P . In this generalization we use inequalities for partial sums associated with ideals in P . Basic properties are established, including connections to classical majorization. Moreover, we investigate transfers (given by doubly stochastic matrices), complexity issue...

A Tutte Polynomial for Partially Ordered Sets

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 ...