Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.04295 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915715381985280 |
|---|---|
| author | Gomes, Paulo Henrique Cunha |
| author_facet | Gomes, Paulo Henrique Cunha |
| contents | We exhibit an explicit family $\mathcal{B}$ of $30$ subsets (``blocks'') of size $6$ of $[60]=\{1,2,\dots,60\}$ with the following property: for every $6$-subset $S\subset[60]$, there exists a block $B\in\mathcal{B}$ such that $|S\cap B|\ge 2$. The construction is fully explicit and the proof is purely combinatorial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04295 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An explicit family of 30 blocks meeting every 6-set of [60] in at least two points Gomes, Paulo Henrique Cunha Combinatorics We exhibit an explicit family $\mathcal{B}$ of $30$ subsets (``blocks'') of size $6$ of $[60]=\{1,2,\dots,60\}$ with the following property: for every $6$-subset $S\subset[60]$, there exists a block $B\in\mathcal{B}$ such that $|S\cap B|\ge 2$. The construction is fully explicit and the proof is purely combinatorial. |
| title | An explicit family of 30 blocks meeting every 6-set of [60] in at least two points |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.04295 |