Can I read Integer Colorings with Forbidden Rainbow Sums on EtoBox?

Integer Colorings with Forbidden Rainbow Sums by Cheng, Yangyang; Jing, Yifan; Li, Lina; Wang, Guanghui; Zhou, Wenling is a scholarly article available to read on EtoBox.

What is Integer Colorings with Forbidden Rainbow Sums about?

For a set of positive integers $A \subseteq [n]$, an $r$-coloring of $A$ is rainbow sum-free if it contains no rainbow Schur triple. In this paper we initiate the study of the rainbow Erd\H{o}s-Rothchild problem in the context of sum-free sets, which asks for the subsets of $[n]$ with the maximum number of rainbow sum-free $r$-colorings. We show that for $r=3$, the interval $[n]$ is optimal, while for $r\geq8$, the set $[\lfloor n/2 \rfloor, n]$ is optimal. We also prove a stability theorem for $r\geq4$. The proofs rely on the hypergraph container method, and some ad-hoc stability analysis.

Author

Cheng, Yangyang; Jing, Yifan; Li, Lina; Wang, Guanghui; Zhou, Wenling

Published

2020

Language

EN