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authorChris Wells <chris@mathematicaster.org>2026-02-04 07:31:03 -0600
committerChris Wells <chris@mathematicaster.org>2026-02-04 07:31:03 -0600
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@@ -1,4 +1,4 @@
-@unpublished{briggs_vietoris,
+@article{briggs_vietoris,
title = {Facets in the Vietoris&ndash;Rips complexes of hypercubes},
author = {Briggs, Joseph and Feng, Ziqin},
month = {mar},
@@ -11,7 +11,7 @@
abstract = {In this paper, we investigate the facets of the Vietoris&ndash;Rips complex $\mathcal{VR}(Q_n; r)$ where $Q_n$ denotes the $n$-dimensional hypercube. We are particularly interested in those facets which are somehow independent of the dimension $n$. Using Hadamard matrices, we prove that the number of different dimensions of such facets is a super-polynomial function of the scale $r$, assuming that $n$ is sufficiently large. We show also that the $(2r-1)$-th dimensional homology of the complex $\mathcal{VR}(Q_n; r)$ is non-trivial when $n$ is large enough, provided that the Hadamard matrix of order $2r$ exists.},
}
-@unpublished{briggs_frogs,
+@article{briggs_frogs,
title = {Frogs, hats and common subsequences},
author = {Briggs, Joseph and Parker, Alex and Schwieder, Coy},
month = {apr},
@@ -24,7 +24,7 @@
}
-@unpublished{briggs_phases,
+@article{briggs_phases,
author = {Briggs, Joseph},
title = {Phase transitions in isoperimetric problems on the integers},
year = {2024},
@@ -37,7 +37,7 @@
abstract = {Barber and Erde asked the following question: if $B$ generates $\mathbb Z^n$ as an additive group, then must the extremal sets for the vertex/edge-isoperimetric inequality on the Cayley graph $\operatorname{Cay}(\mathbb Z^n,B)$ form a nested family? We answer this question negatively for both the vertex- and edge-isoperimetric inequalities, specifically in the case of $n=1$. The key is to show that the structure of the cylinder $\mathbb Z\times(\mathbb Z/k\mathbb Z)$ can be mimicked in certain Cayley graphs on $\mathbb Z$, leading to a phase transition. We do, however, show that Barber&ndash;Erde's question for Cayley graphs on $\mathbb Z$ has a positive answer if one is allowed to ignore finitely many sets.}
}
-@unpublished{heath_oddcycles,
+@article{heath_oddcycles,
author = {Heath, Emily and Martin, Ryan R.},
title = {The maximum number of odd cycles in a planar graph},
year = {2025},