Solution of a research problem on trees of subsets (Q1335406)
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scientific article; zbMATH DE number 646767
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solution of a research problem on trees of subsets |
scientific article; zbMATH DE number 646767 |
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Solution of a research problem on trees of subsets (English)
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12 February 1995
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Let \(X\) be an \(n\)-element set and \(\mathcal F\) a \(k\)-element collection of proper, non-empty subsets of \(X\) such that if \(A\), \(B\in {\mathcal F}\) then either \(A\subseteq B\), or \(B\subseteq A\), or they are disjoint. A closed formula is given for the number of those collections and it is shown that \(k\leq 2n-2\).
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trees of subsets
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extremal set theory
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enumeration
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