论文标题
有限环上的点产品集和简单
Dot-product sets and simplices over finite rings
论文作者
论文摘要
在本文中，我们在有限环上研究了矢量空间中的点产品集和$ k $ -simplices。我们表明，如果$ e $足够大，那么$ e $的点产品集涵盖了整个戒指。在较高维度的情况下，如果$ e $足够大，那么由$ e $确定的一组简单和一组点产品简单，直到富集，具有正密度。
In this paper, we study dot-product sets and $k$-simplices in vector spaces over finite rings. We show that if $E$ is sufficiently large then the dot-product set of $E$ covers the whole ring. In higher dimensional cases, if $E$ is sufficiently large then the set of simplices and the set of dot-product simplices determined by $E$, up to congurence, have positive densities.
