3 papers
math.CO2024
Chain Conditions and Optimal Elements in Generalized Union-Closed Families of Sets
Cory H. Colbert
The union-closed sets conjecture (sometimes referred to as Frankl's conjecture) states that every finite, nontrivial union-closed family of sets has an element that is in at least…
math.AC2021
A Structural Invariant On Certain Two-Dimensional Noetherian Partially Ordered Sets
Cory Colbert
If is a partially ordered set satisfying certain necessary conditions for to be order-isomorphic to the spectrum of a Noetherian domain of dimension two, we descri…
math.AC2018
On Two Dimensional Semi-Local Noetherian Spectra
Cory H. Colbert
In this article, we develop a technique to "split" certain types of partially ordered sets into simpler ones and use that technique to give a partial answer to a conjecture by R. W…