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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.05917 |
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| _version_ | 1866908638642176000 |
|---|---|
| author | Nguyen, Tuan |
| author_facet | Nguyen, Tuan |
| contents | We provide a characterization of maximal left-compressed families based on their generating sets $\mathcal{G}\subseteq 2^{[n]}$. We show that there is a one-to-one correspondence between maximal left-compressed families $\mathcal{A}\subseteq \binom{[n]}{k}$ and principal generating sets. Moreover, we give a complete description of maximal left-compressed intersecting families having exactly two maximal generators. Based on this, for any $X\subseteq [2,n]$, we compare $\mathcal{A}(X)$, where $\mathcal{A}$ is a rank-2 maximal left-compressed intersecting family with exactly two maximal generators, and $\mathcal{S}(X)$, where $\mathcal{S}$ denotes the Star family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Maximal Left-Compressed Intersecting Families Generated by a Collection of Subsets of [$n$] Nguyen, Tuan Combinatorics We provide a characterization of maximal left-compressed families based on their generating sets $\mathcal{G}\subseteq 2^{[n]}$. We show that there is a one-to-one correspondence between maximal left-compressed families $\mathcal{A}\subseteq \binom{[n]}{k}$ and principal generating sets. Moreover, we give a complete description of maximal left-compressed intersecting families having exactly two maximal generators. Based on this, for any $X\subseteq [2,n]$, we compare $\mathcal{A}(X)$, where $\mathcal{A}$ is a rank-2 maximal left-compressed intersecting family with exactly two maximal generators, and $\mathcal{S}(X)$, where $\mathcal{S}$ denotes the Star family. |
| title | On Maximal Left-Compressed Intersecting Families Generated by a Collection of Subsets of [$n$] |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.05917 |