6 citations · 18 across the 13 of their papers we have counts for
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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…
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…
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…
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…