Colored Tverberg Theorems for non-prime powers

Leandro V. Mauri; Rade T. Živaljević; Denise de Mattos; Edivaldo L. dos Santos

Colored Tverberg Theorems for non-prime powers

Combinatorics 2022-11-07 v1 Algebraic Topology

Authors: Leandro V. Mauri , Rade T. Živaljević , Denise de Mattos , Edivaldo L. dos Santos

Abstract

We prove a relative of the Optimal (Type B)} Colored Tverberg theorem of \v{Z}ivaljevi\'{c} and Vre\'{c}ica 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 $\vert C_i\vert \in \{2q-2, 2q+1\}$ while in the original theorem $\vert C_i\vert = 2q-1$ for all $i$ .

Keywords

ramsey theory and colorings

Cite

@article{arxiv.2211.02078,
  title  = {Colored Tverberg Theorems for non-prime powers},
  author = {Leandro V. Mauri and Rade T. Živaljević and Denise de Mattos and Edivaldo L. dos Santos},
  journal= {arXiv preprint arXiv:2211.02078},
  year   = {2022}
}

Comments

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

Colored Tverberg Theorems for non-prime powers

Abstract

Keywords

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