← 研踪 PaperTrailarXiv:2611.05568 · v1
Non-redundant Independence Atoms
首次提交 2026-11-04 04:01
版本更新 2026-11-04 04:01
雷达观测 2026-11-05 10:08
摘要
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.
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v1 · 2026-11-04 04:01 · 最新观测版本
Non-redundant Independence Atoms
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.
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