Colored Tverberg Theorems for Non-prime Powers
Abstract
We prove a relative of both the original and the optimal (Type B) version of the Colored Tverberg theorem of Živaljević and Vrećica (Theorems ?? and ??), which modifies these results in two different ways. (1) We extend the original theorems beyond the prime powers by showing that the theorem is valid if the number of rainbow faces is q = pn − 1. (2) The size of some rainbow simplices may be smaller than in the original theorems. More precisely |Ci|∈{2q − 2,2q + 1} while (for comparison) in the original theorems it is |Ci| = 2q − 1. The proof relies on equivariant index theory and a result of Volovikov [?] about partial coincidences of maps f : X → ℝd, from a G-space into the Euclidean space.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Finite Group Theory Research
graph theory and CDMA systems
Publication details
- Journal / source
- Kragujevac Journal of Mathematics
- Publisher
- University Library in Kragujevac
- Volume
- 50
- Issue
- 4
- Pages
- 645–645
- Publication date
- 3 May 2026
- Language
- EN