The Polychromatic Number of Small Subsets of the Integers Modulo $n$

Emelie Curl; John Goldwasser; Joe Sampson; Michael Young

The Polychromatic Number of Small Subsets of the Integers Modulo $n$

Combinatorics 2020-07-30 v1 Group Theory

Authors: Emelie Curl , John Goldwasser , Joe Sampson , Michael Young

Abstract

If $S$ is a subset of an abelian group $G$ , the polychromatic number of $S$ in $G$ is the largest integer $k$ so that there is a $k-$ coloring of the elements of $G$ such that every translate of $S$ in $G$ gets all $k$ colors. We determine the polychromatic number of all sets of size 2 or 3 in the group of integers mod n.

Keywords

polychromatic number abelian group integers modulo n subset coloring translates

Cite

@article{arxiv.2007.14468,
  title  = {The Polychromatic Number of Small Subsets of the Integers Modulo $n$},
  author = {Emelie Curl and John Goldwasser and Joe Sampson and Michael Young},
  journal= {arXiv preprint arXiv:2007.14468},
  year   = {2020}
}

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