Note as to size-minimal hypercompletly separating systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908855787585536 |
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| author | Batikova, B. Kepka, T. J. Nemec, P. C. |
| author_facet | Batikova, B. Kepka, T. J. Nemec, P. C. |
| contents | If $S$ is a non-empty finite set, $|S|=s$, then a system $\mathscr{A}$ of subsets of $S$ is a size-minimal hypercompletely separable system (i.e., for every $a\in S$ there are $A,B\in\mathscr{A}$ such that $A\cap B=\{a\}$) if and only if $|\mathscr{A}|=\left\lceil\frac{1+\sqrt{8s+1}}2\right\rceil$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23897 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Note as to size-minimal hypercompletly separating systems Batikova, B. Kepka, T. J. Nemec, P. C. Combinatorics 05D05, 05B99, 06E99 If $S$ is a non-empty finite set, $|S|=s$, then a system $\mathscr{A}$ of subsets of $S$ is a size-minimal hypercompletely separable system (i.e., for every $a\in S$ there are $A,B\in\mathscr{A}$ such that $A\cap B=\{a\}$) if and only if $|\mathscr{A}|=\left\lceil\frac{1+\sqrt{8s+1}}2\right\rceil$. |
| title | Note as to size-minimal hypercompletly separating systems |
| topic | Combinatorics 05D05, 05B99, 06E99 |
| url | https://arxiv.org/abs/2602.23897 |