6 citations · 8 across the 9 of their papers we have counts for
9 papers
Quantifying discontinuity
Henry Adams, Florian Frick, Michael Harrison +2
Given a compact space that does not admit an embedding (an injective continuous function) into , we study the ''degree'' of discontinuity that any injective funct…
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
Simplicial complexes from finite projective planes and colored configurations
Matt Superdock
In the 7-vertex triangulation of the torus, the 14 triangles can be partitioned as , such that each represents the lines of a copy of the Fano plane $PG…
Vertex numbers of simplicial complexes with free abelian fundamental group
Florian Frick, Matt Superdock
We show that the minimum number of vertices of a simplicial complex with fundamental group is at most and at least . For the upper bound, we use…
Clean tangled clutters, simplices, and projective geometries
Ahmad Abdi, Gérard Cornuéjols, Matt Superdock
A clutter is \emph{clean} if it has no delta or the blocker of an extended odd hole minor, and it is \emph{tangled} if its covering number is two and every element appears in a min…
A nonlinear Lazarev-Lieb theorem: -orthogonality via motion planning
Florian Frick, Matt Superdock
Lazarev and Lieb showed that finitely many integrable functions from the unit interval to can be simultaneously annihilated in the inner product by a smooth func…
Predicting outcomes for games of skill by redefining what it means to win
J. Scott Moreland, Matthew C. Superdock
The Elo rating system is a highly successful ranking algorithm for games of skill where, by construction, one team wins and the other loses. A primary limitation of the original El…
The Graceful Tree Conjecture: a class of graceful diameter-6 trees
Matthew C. Superdock
We survey the current state of progress on the Graceful Tree Conjecture, and then we present several new results toward the conjecture, driven by three new ideas: (1) It has been p…
New graceful diameter-6 trees by transfers
Matt Superdock
Given a graph , a labeling of is an injective function . Under the labeling , the label of a vertex is , and the induced la…