Correlation inequalities on some 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.

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...

Some Results on Linear Discrepancy for Partially Ordered Sets

To my parents, Jim and Karol, who believed a farm kid from North Dakota could do whatever he wanted and helped me achieve whatever I imagined and more. iii ACKNOWLEDGEMENTS There are many people without whose mentoring, guidance, support, and friendship this dissertation never would have been written. My advisor, William T. Trotter, is at the top of that list. I have greatly enjoyed working wit...

Linear Inequalities for Enumerating Chains in Partially Ordered Sets

We characterize the linear inequalities satisfied by flag f -vectors of all finite bounded posets. We do the same for semipure posets. In particular, the closed convex cone generated by flag f -vectors of bounded posets of fixed rank is shown to be simplicial, and the closed cone generated by flag f -vectors of semipure posets of fixed rank is shown to be polyhedral. The extreme rays of both of...