Families without $s$-matchings: the other end
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917454095056896 |
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| author | Kupavskii, Andrey Sokolov, Georgy |
| author_facet | Kupavskii, Andrey Sokolov, Georgy |
| contents | In this paper, we determine the largest family $\mathcal F \subset 2^{[n]}$ without $s$ pairwise disjoint sets, provided $n=ms+c$ for positive integers $m,c$, and $s \geq s_0(m, c)$. This result can be seen as a non-uniform analogue of the results on the Erd\H os Matching Conjecture in the regime when the clique is extremal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Families without $s$-matchings: the other end Kupavskii, Andrey Sokolov, Georgy Combinatorics Discrete Mathematics In this paper, we determine the largest family $\mathcal F \subset 2^{[n]}$ without $s$ pairwise disjoint sets, provided $n=ms+c$ for positive integers $m,c$, and $s \geq s_0(m, c)$. This result can be seen as a non-uniform analogue of the results on the Erd\H os Matching Conjecture in the regime when the clique is extremal. |
| title | Families without $s$-matchings: the other end |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2605.00996 |