论文标题
有限的家族没有其他人的结合涵盖的家族
Families of finite sets in which no set is covered by the union of the others
论文作者
论文摘要
让F成为有限的有限非空套家族。我们证明了以下内容：（i）F满足标题的状况，并且仅当每对不同的subfimilies {a_1，...，...，a_r}，{b_1，...，...，...，b_s} f与a_i的结合不同于b_i的联合。 （ii）如果f满足标题的条件，则奇怪的是，f包含至少一组f的f成员的联合子集的数量是奇数。我们给出了这些结果的两个应用，一个是数字理论，另一个是交换代数。
Let F be a finite nonempty family of finite nonempty sets. We prove the following: (i) F satisfies the condition of the title if and only if for every pair of distinct subfamilies {A_1,...,A_r}, {B_1,...,B_s} of F, the union of the A_i is different from the union of the B_i. (ii) If F satisfies the condition of the title, then the number of subsets of the union of the members of F containing at least one set of F is odd. We give two applications of these results, one to number theory and one to commutative algebra.
