Colored Tverberg Theorems for non-prime powers

Abstract

We prove a relative of the Optimal (Type B)} Colored Tverberg theorem of Živaljević and Vrećica which modifies this results in two different ways. (1) Our result is valid if the number of rainbow faces is $q=p^n-1$, where $p$ is a prime. (2) The size of rainbow simplices satisfies the condition $|C_i|\in \{2q-2,2q+1\}$ while in the original theorem $|C_i|=2q-1$ for all $i$.

arXiv admin note: text overlap with arXiv:2210.09101, arXiv:2210.07804