J. Briggs

collaborators

4 papers

math.MG2026

Isoperimetric Inequalities in the $ℓ_{\infty}$ cube and torus

Ben Baker, Joseph Briggs, Manuel Fernandez +1

We prove an exact isoperimetric inequality for cubes and tori under the $\ell_{\infty} metric. As a corollary, we recover the celebrated grid edge-isoperimetric inequality of Bollo…

math.AT2024

Facets in the Vietoris--Rips complexes of hypercubes

Joseph Briggs, Ziqin Feng, Chris Wells

In this paper, we investigate the facets of the Vietoris--Rips complex $V R (Q_{n}; r)$ where $Q_{n}$ denotes the $n$ -dimensional hypercube. We are particularly interested in t…

math.CO2024

Frogs, hats and common subsequences

Joseph Briggs, Alex Parker, Coy Schwieder +1

Write $W^{(n)}$ to mean the $n$ -letter word obtained by repeating a fixed word $W$ and let $R_{n}$ denote a uniformly random $n$ -letter word sampled from the same alphabet as $W$ . We…

math.CO2024

Phase transitions in isoperimetric problems on the integers

Joseph Briggs, Chris Wells

Barber and Erde asked the following question: if $B$ generates $Z^{d}$ as an additive group, then must the extremal sets for the vertex/edge-isoperimetric inequality on the C…

Isoperimetric Inequalities in the ℓ∞​ cube and torus

Facets in the Vietoris--Rips complexes of hypercubes

Frogs, hats and common subsequences

Phase transitions in isoperimetric problems on the integers

Isoperimetric Inequalities in the $ℓ_{\infty}$ cube and torus