6 papers
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…
Rigid-flexible values for symplectic embeddings of four-dimensional ellipsoids into almost-cubes
Andrew Lee, Cory H. Colbert
We consider the embedding function describing the problem of symplectically embedding an ellipsoid into the smallest possible scaling by of the polydisc $P(…
Every Finite Poset is Isomorphic to a Saturated Subset of the Spectrum of a Noetherian UFD
Cory H. Colbert, S. Loepp
We show that every finite poset is isomorphic to a saturated subset of the spectrum of a Noetherian unique factorization domain. In addition, we show that every finite poset is iso…
Gluing Minimal Prime Ideals in Local Rings
Cory H. Colbert, S. Loepp
Let be a reduced local (Noetherian) ring with maximal ideal . Suppose that contains the rationals, is uncountable and . Let the minimal prime ideals o…
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…
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…