报告题目：Complete solution to a conjecture of Butler, Costello, and Graham

报告人：毛亚平 教授，青海师范大学

时间地点：五教5101

报告时间：10月12日 上午10：10-10：50

摘要：

In 2010, Butler, Costello, and Graham proposed a conjecture: Let $ax + by = az$ be an equation, where $a, b$ are integers. Denote by $R,B$ the colors red and blue, respectively. $(i)$ If $b>a\geq 2$ and $\gcd(a, b)=1$, then the coloring that gives the minimum number of monochromatic solutions over any $2$-coloring of $[1, n]$ is $[(R^{a-1}, B)^{\frac{n}{b}},R^{(\frac{b-a}{b})n}]$. $(ii)$ If $a>b\geq 2$ and $\gcd(a, b)=1$, then the coloring that gives the minimum number of monochromatic solutions over any $2$-coloring of $[1, n]$ is $[(R^{a-1}, B)^{\frac{n}{a}}]$. We completely confirm this conjecture. This is a joint work with Gang Yang.