2024/12/20 by Andreas F. Holmsen, Grace McCourt, Holmsen, Andreas F. +5 · 1 citation
Computer Science · #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2412.16055
openalex publication_date 2024/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let Δ denote the 8-dimensional simplex viewed as an abstract simplicial complex, and suppose that its vertices are arranged in a 3× 3 array. Then for any continuous map f:Δ→ ℝ3 it is possible to partition the rows or the columns of the vertex array into two parts, such that the disjoint faces σ and τ induced by the two parts satisfy f(σ)∩ f(τ) ≠ ∅. Our result also has consequences for geometric transversals and topological Helly.