Brent Holmes

activity

20162018

most citedOn the diameter of dual graphs of Stanley-Reisner rings with Serre

(S_{2})

property and Hirsch type bounds on abstractions of polytopes

2 citations · 3 across the 2 of their papers we have counts for

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math.AC2018

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…

math.AC2017

A Generalized Serre's Condition

Brent Holmes

Throughout, let $R$ be a commutative Noetherian ring. A ring $R$ satisfies Serre's condition $(S_{ℓ})$ if for all $P \in \Spec R,$ $\depth R_P \geq \min \{ \ell , \dim R_P \}$.…

math.AC2016★ 2 cited

On the diameter of dual graphs of Stanley-Reisner rings with Serre $(S_{2})$ property and Hirsch type bounds on abstractions of polytopes

Brent Holmes

Let $R$ be a Noetherian commutative ring of positive dimension. The Hochster-Huneke graph of $R$ (sometimes called the dual graph of Spec $R$ and denoted by $G (R)$ ) is d…

Rank Selection and Depth Conditions for Balanced Simplicial Complexes

A Generalized Serre's Condition

On the diameter of dual graphs of Stanley-Reisner rings with Serre (S2​) property and Hirsch type bounds on abstractions of polytopes

On the diameter of dual graphs of Stanley-Reisner rings with Serre $(S_{2})$ property and Hirsch type bounds on abstractions of polytopes