New formulations of the union-closed sets conjecture
The union-closed sets conjecture states that if a finite set $\mathcal A$ of finite sets is union-closed and $\mathcal A\neq \{ \varnothing\}$, then there exists an element in $\displaystyle\cup_{A\in \mathcal A} A$ that belongs to at least half of the sets in $\mathcal A$. We present three new fo...
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| Format: | Article |
| Language: | English |
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American Journal of Combinatorics
2022-02-01
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| Series: | The American Journal of Combinatorics |
| Subjects: | |
| Online Access: | https://ajcombinatorics.org/Volume1/V1.03.pdf |
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| Summary: | The union-closed sets conjecture states that if a finite set $\mathcal A$ of finite sets is union-closed and $\mathcal A\neq \{ \varnothing\}$, then there exists an element in $\displaystyle\cup_{A\in \mathcal A} A$ that belongs to at least half of the sets in $\mathcal A$. We present three new formulations of the union-closed conjecture in terms of matrices, graphs, and hypergraphs. |
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| ISSN: | 2768-4202 |