报告题目：Integer colorings with no rainbow $k$-term arithmetic progression

报告人：周文玲

报告时间：2022.10.1下午15:30-16:30

报告地点：腾讯会议889845730

摘要：In this talk, we study the rainbow Erd\H{o}s-Rothschild problem with respect to $k$-term arithmetic progressions. For a set of positive integers $S \subseteq [n]$,

an $r$-coloring of $S$ is \emph{rainbow $k$-AP-free} if it contains no rainbow $k$-term arithmetic progression. Let $g_{r,k}(S)$ denote the maximum number of rainbow $k$-AP-free $r$-colorings of $S$. For sufficiently large $n$ and fixed integers $r\ge k\ge 3$, we show that $g_{r,k}(S)<g_{r,k}([n])$ for any proper subset $S\subset [n]$. Further, we prove that $\lim_{n\to \infty}g_{r,k}([n])/(k-1)^n= \binom{r}{k-1}$. Our result is asymptotically best possible and implies that, almost all rainbow $k$-AP-free $r$-colorings of $[n]$ use only $k-1$ colors.

报告人简介：周文玲，山东大学和巴黎萨克雷大学联合培养博士生，师从王光辉教授和李皓教授。主要研究方向是极值组合，包括：染色图与有向图的Tur\'an 问题，拟随机超图的 Tur\'an 问题和Factor 问题以及一些整数集合中的极值问题等。已经在Journal of the London Mathematical Society和European Journal of Combinatorics等杂志发表3篇文章。