和集问题是加法组合中的重要研究方向，而 Cauchy-Davenport 定理是和集问题中最经典的结果之一。从线性代数角度理解，Cauchy-Davenport 定理可以看做是关于 A×B 在映射 +：Fp×Fp →Fp 下的像集基数大小的描述。本项目中我们拟对于更一般的线性映射, 研究其像集基数的大小。

The sumset problem is the main part of additive combinatorics , and the Cauchy-Davenport theorem is a fundamental result. From the view of linear algebra, the Cauchy-Davenport theorem can be seen as a statement about the size of the image of the product set A×B under the map +：Fp×Fp →Fp. We plan to study the size of the image of for general linear maps.