论文标题
避免在$ \ mathbb {z} _6^n $中避免六项算术进程的集合是指数级的
Sets avoiding six-term arithmetic progressions in $\mathbb{Z}_6^n$ are exponentially small
论文作者
论文摘要
我们显示的是避免在$ \ mathbb {z} _6^n $中避免6-期算术进程的大小最多$ 5.709^n $。还可以指出的是，在这种情况下，“产品构建”不起作用，特别是，我们表明，对于极小尺寸的极小尺寸，我们有$ r_6（\ mathbb {z} _6 _6）= 5 $，$ r_6（\ mathbb {z} _66^2）= 25 $ and $ 116 \ le q r_6（Z 6（Z 6） 124 $。
We show that sets avoiding 6-term arithmetic progressions in $\mathbb{Z}_6^n$ have size at most $5.709^n$. It is also pointed out that the "product construction" does not work in this setting, specially, we show that for the extremal sizes in small dimensions we have $r_6(\mathbb{Z}_6)=5$, $r_6(\mathbb{Z}_6^2)=25$ and $ 116\leq r_6(\mathbb{Z}_6^3)\leq 124$.
