2 citations · 3 across the 8 of their papers we have counts for
9 papers
Homology of Vietoris-Rips complexes of hypercube graphs via group actions
Federico Galetto, Jonathan Montaño, Zoe Wellner
The Vietoris-Rips complex of a metric space is the simplicial complex whose faces are the subsets of points with pairwise distance bounded above by a given scale . In this paper…
Classification of equiangular lines with fixed angle
Theodore Gossett, Zilin Jiang, Adam Teets +1
We determine the maximum number of equiangular lines with fixed angle for in -dimensional Euclidean space: $2,3,4,6,8,10,14,15,16,17,18,20…
Covering and labeling generalizations of the Borsuk-Ulam theorem
Florian Frick, Zoe Wellner
We prove multiple generalizations of Fan's combinatorial labeling result for sphere triangulations. This can be seen as a comprehensive extension of the Borsuk--Ulam theorem. In ty…
Topological methods in zero-sum Ramsey theory
Florian Frick, Jacob Lehmann Duke, Meenakshi McNamara +5
A cornerstone result of Erd\H os, Ginzburg, and Ziv (EGZ) states that any sequence of elements in contains a zero-sum subsequence of length . While algebra…
Colorful Borsuk--Ulam theorems and applications
Florian Frick, Zoe Wellner
We prove a colorful generalization of the Borsuk--Ulam theorem and derive colorful consequences from it, such as a colorful generalization of the ham sandwich theorem. Even in the…
New families of simplicial filtration functors
Samir Chowdhury, Nathaniel Clause, Facundo Memoli +2
The so called Čech and Vietoris-Rips simplicial filtrations are designed to capture information about the topological structure of metric datasets. These filtrations are two of the…
Flow polytopes of partitions
Karola Mészáros, Connor Simpson, Zoe Wellner
Recent progress on flow polytopes indicates many interesting families with product formulas for their volume. These product formulas are all proved using analytic techniques. Our w…
Fair division and generalizations of Sperner- and KKM-type results
Megumi Asada, Florian Frick, Vivek Pisharody +4
We treat problems of fair division, their various interconnections, and their relations to Sperner's lemma and the KKM theorem as well as their variants. We prove extensions of Alo…
On Reay's relaxed Tverberg conjecture and generalizations of Conway's thrackle conjecture
Megumi Asada, Ryan Chen, Florian Frick +5
Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in E…