Colored Tverberg Theorems for non-prime powers

2022/11/03 by Mauri, Leandro V., Živaljević, Rade T., de Mattos, Denise +1
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.02078

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= pⁿ-1, where p is a prime. (2) The size of rainbow simplices satisfies the condition \vert C_i\vert ∈ \2q-2, 2q+1\ while in the original theorem \vert C_i\vert = 2q-1 for all i.

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