A Note on the Union-closed Sets Conjecture
Let $M$ be a non-zero binary matrix with distinct rows where the rows are closed under certain logical operators. In this article, we investigate the existence of columns containing an equal or greater number of ones than zeros. Specifically, the existence of such columns when the rows of the matrix...
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| Main Author: | |
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| Format: | Journal Article |
| Language: | English |
| Published: |
04-09-2023
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | Let $M$ be a non-zero binary matrix with distinct rows where the rows are
closed under certain logical operators. In this article, we investigate the
existence of columns containing an equal or greater number of ones than zeros.
Specifically, the existence of such columns when the rows of the matrix are
closed under $\textit{material conditional}$ leads us to a weaker version of
the $\textit{Union-Closed Set Conjecture}$. |
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| DOI: | 10.48550/arxiv.2309.01704 |