On set systems without singleton intersections
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916342637002752 |
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| author | Cherkashin, Danila |
| author_facet | Cherkashin, Danila |
| contents | Consider a family $\mathcal{F}$ of $k$-subsets of an ambient $(k^2-k+1)$-set such that no pair of $k$-subsets in $\mathcal{F}$ intersects in exactly one element. In this short note we show that the maximal size of such $\mathcal{F}$ is $\binom{k^2-k-1}{k-2}$ for every $k > 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On set systems without singleton intersections Cherkashin, Danila Combinatorics Consider a family $\mathcal{F}$ of $k$-subsets of an ambient $(k^2-k+1)$-set such that no pair of $k$-subsets in $\mathcal{F}$ intersects in exactly one element. In this short note we show that the maximal size of such $\mathcal{F}$ is $\binom{k^2-k-1}{k-2}$ for every $k > 1$. |
| title | On set systems without singleton intersections |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.00484 |