A proof of the union-close set conjecture
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866915846968836096 |
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| author | Agama, Theophilus |
| author_facet | Agama, Theophilus |
| contents | In this paper, we introduce the notion of the universe, induced communities, and cells with their corresponding spots. Using this language, we formulate and prove the union close set conjecture by showing that for any finite universe $\mathbb{U}$ and any induced community $\mathcal{M}_{\mathbb{U}}$ there exist some spot $a\in \mathbb{U}$ such that the density \begin{align} \mathcal{D}_{\mathcal{M}_{\mathbb{U}}}(a)\geq \frac{1}{2}.\nonumber \end{align} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_02665 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A proof of the union-close set conjecture Agama, Theophilus General Mathematics In this paper, we introduce the notion of the universe, induced communities, and cells with their corresponding spots. Using this language, we formulate and prove the union close set conjecture by showing that for any finite universe $\mathbb{U}$ and any induced community $\mathcal{M}_{\mathbb{U}}$ there exist some spot $a\in \mathbb{U}$ such that the density \begin{align} \mathcal{D}_{\mathcal{M}_{\mathbb{U}}}(a)\geq \frac{1}{2}.\nonumber \end{align} |
| title | A proof of the union-close set conjecture |
| topic | General Mathematics |
| url | https://arxiv.org/abs/1711.02665 |