6 citations · 18 across the 13 of their papers we have counts for
14 papers
Topological Tverberg theorems for products of polytopes
Steven Simon
The topological Tverberg theorem asserts that if is a prime power then for any continuous map from the -dimensional…
The Generalized Makeev Problem Revisited
Andres Mejia, Steven Simon, Jialin Zhang
Based on a result of Makeev, in 2012 Blagojević and Karasev proposed the following problem: given any positive integers and , find the minimum dimension $d=Δ(…
Transversal generalizations of hyperplane equipartitions
Florian Frick, Samuel Murray, Steven Simon +1
The classical Ham Sandwich theorem states that any point sets in can be simultaneously bisected by a single affine hyperplane. A generalization of Dolnikov asser…
Straightening Out the Frobenius-Schur Indicator
Steven H. Simon, Joost K. Slingerland
The Frobenius-Schur indicator is a parameter assigned to each self-dual particle in a TQFT. If is negative then straightening out a timelike zig-zag in the wo…
Inscribed Tverberg-Type Partitions for Orbit Polytopes
Steven Simon, Tobias Timofeyev
Tverberg's theorem states that any set of points in can be partitioned into subsets whose convex hulls have non-empty -fold intersection…
Embedding dimensions of simplicial complexes on few vertices
Florian Frick, Mirabel Hu, Verity Scheel +1
We provide a simple characterization of simplicial complexes on few vertices that embed into the -sphere. Namely, a simplicial complex on vertices embeds into the -sphe…
Regular Polygonal Partitions of a Tverberg Type
Leah Leiner, Steven Simon
A seminal theorem of Tverberg states that any set of points in can be partitioned into subsets whose convex hulls have non-empty -fold i…
Hyperplane Equipartitions Plus Constraints
Steven Simon
While equivariant methods have seen many fruitful applications in geometric combinatorics, their inability to answer the now settled Topological Tverberg Conjecture has made appare…
Measure Partitions via Fourier Analysis II: Center Transversality in the -norm for Complex Hyperplanes
Steven Simon
Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtai…
Average-Value Tverberg Partitions via Finite Fourier Analysis
Steven Simon
The long-standing topological Tverberg conjecture claimed, for any continuous map from the boundary of an -simplex to -dimensional Euclidian space, the exist…
Measure Equipartitions via Finite Fourier Analysis
Steven Simon
Applications of harmonic analysis on finite groups are introduced to measure partition problems, with equipartitions obtained as the vanishing of prescribed Fourier transforms. For…
Equivariant Equipartitions: Ham Sandwich Theorems for Finite Subgroups of Spheres
Steven Simon
Equivariant "Ham Sandwich" Theorems are obtained for the finite subgroups G of the unit spheres S(F) in the classical algebras F = R, C, and H. Given any n F-valued mass distributi…
A Ham Sandwich Analogue for Quaternionic Measures and Finite Subgroups of S^3
Steven Simon
A "ham sandwich" theorem is established for n quaternionic Borel measures on quaternionic space H^n. For each finite subgroup G of S^3, it is shown that there is a quaternionic hyp…
From the Ham Sandwich to the Pizza Pie: A Simultaneous Z_m Equipartition of Complex Measures
Steven Simon
A "ham sandwich" theorem is derived for n complex Borel measures on C^n. For each integer m>=2, it shown that there exists a regular m-fan centered about a complex hyperplane, sati…