2 citations · 3 across the 2 of their papers we have counts for
4 papers
Rank Selection and Depth Conditions for Balanced Simplicial Complexes
Brent Holmes, Justin Lyle
We prove some new rank selection theorems for balanced simplicial complexes. Specifically, we prove that rank selected subcomplexes of balanced simplicial complexes satisfying Serr…
Higher Nerves of Simplicial Complexes
Hailong Dao, Joseph Doolittle, Ken Duna +3
We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of t…
A Generalized Serre's Condition
Brent Holmes
Throughout, let be a commutative Noetherian ring. A ring satisfies Serre's condition if for all $P \in \Spec R,$ $\depth R_P \geq \min \{ \ell , \dim R_P \}$.…
On the diameter of dual graphs of Stanley-Reisner rings with Serre property and Hirsch type bounds on abstractions of polytopes
Brent Holmes
Let be a Noetherian commutative ring of positive dimension. The Hochster-Huneke graph of (sometimes called the dual graph of Spec and denoted by ) is d…