Decompositions of Modules Associated to Finite Partially 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.

On Algebras Associated to Partially Ordered Sets

We continue the study [2] on sheaves of rings on finite posets. We present examples where the ring of global sections coincide with toric faces rings, quotients of a polynomial ring by a monomial ideal and algebras with straightening laws. We prove a rank-selection theorem which generalizes the well-known rank-selection theorem of Stanley–Reisner rings. Finally, we determine an explicit present...

Closure Operators Associated to Partially Ordered Sets

Interactive Computation of Homology of Finite Partially Ordered Sets

We outline a method for practical use of an interactive system (APL) to compute the homology of finite partially ordered sets. 1. Prerequisites. All partially ordered sets (posets) are assumed finite. Given a poset , we say that b covers a if b > a and a g c ^ h implies a = c or b = c. Since we deal with finite posets, the order relation can be obtained as the reflexive, transitive clos...

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 ...