Independence atom is a key concept in relational database theory. In the present paper, we prove that the maximum possible size of a non-redundant set of independence atoms on $n$ attributes is asymptotically $(1+o(1))\binom{n}{\floor{n/2}}$. It turns out that this problem is closely related to two extremal set theory problems, the Katona-Tarján question on ``V''-free families of subsets of $[n]$ for the lower bound, and Kleitman's bound on union-free families for the upper bound.

翻译：暂无翻译