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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.06179 |
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| _version_ | 1866909986460794880 |
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| author | Gomes, Paulo Henrique Cunha |
| author_facet | Gomes, Paulo Henrique Cunha |
| contents | We present an explicit family $\mathcal{B}$ of $920$ subsets of size $6$ of $[60]=\{1,\dots,60\}$ with the property that every $6$-subset $S\subset[60]$ intersects at least one block $B\in\mathcal{B}$ in at least three elements, i.e.\ $|S\cap B|\ge 3$. The construction is purely combinatorial, based on a partition of the ground set into pairs and a pigeonhole argument. We also record a simple counting lower bound and discuss how different partitions of the ten base blocks affect the emergence of triple intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A 920-block explicit construction guaranteeing a triple intersection with every 6-subset of [60] Gomes, Paulo Henrique Cunha Combinatorics We present an explicit family $\mathcal{B}$ of $920$ subsets of size $6$ of $[60]=\{1,\dots,60\}$ with the property that every $6$-subset $S\subset[60]$ intersects at least one block $B\in\mathcal{B}$ in at least three elements, i.e.\ $|S\cap B|\ge 3$. The construction is purely combinatorial, based on a partition of the ground set into pairs and a pigeonhole argument. We also record a simple counting lower bound and discuss how different partitions of the ten base blocks affect the emergence of triple intersections. |
| title | A 920-block explicit construction guaranteeing a triple intersection with every 6-subset of [60] |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.06179 |