关于f-free子集

On f-free Subsets

在整数集或有理数域Ｑ上的向量空间的有限子集上建立了几个函数，证明了这些函数在整数集合内取得它们的最小值。作为它们的一个推论，证明了特征为零的任何非零元素的有限集合都包含一个ｓｕｍ－ｆｒｅｅ子集Ｂ，｜Ｂ｜＞１３｜Ａ｜．

In this paper, several functions are extablished on finite subsets of a vector space over the rational number field Q, or in the integer set. It also verifies that these functions can attain their minimal values within the integer set. Based on this inferred consequence from them, the paper shows us that any finite set A of nonzero elements being characterized by 0 contains a sum-free subset B, with |B|>13|A|.