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Diffstat (limited to 'data/papers.bib')
| -rw-r--r-- | data/papers.bib | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/data/papers.bib b/data/papers.bib index aa2e186..36ad8ea 100644 --- a/data/papers.bib +++ b/data/papers.bib @@ -1,4 +1,4 @@ -@unpublished{briggs_vietoris, +@article{briggs_vietoris, title = {Facets in the Vietoris–Rips complexes of hypercubes}, author = {Briggs, Joseph and Feng, Ziqin}, month =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–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r)$ is non-trivial when $n$ is large enough, provided that the Hadamard matrix of order $2r$ exists.}, } -@unpublished{briggs_frogs, +@article{briggs_frogs, title = {Frogs, hats and common subsequences}, author = {Briggs, Joseph and Parker, Alex and Schwieder, Coy}, month = {apr}, @@ -24,7 +24,7 @@ } -@unpublished{briggs_phases, +@article{briggs_phases, author = {Briggs, Joseph}, title = {Phase transitions in isoperimetric problems on the integers}, year = {2024}, @@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–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question for Cayley graphs on $\mathbb Z$ has a positive answer if one is allowed to ignore finitely many sets.} } -@unpublished{heath_oddcycles, +@article{heath_oddcycles, author = {Heath, Emily and Martin, Ryan R.}, title = {The maximum number of odd cycles in a planar graph}, year =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}, |