Thresholds for $(n,q,2)$-Steiner Systems via Refined Absorption
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917599892209664 |
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| author | Delcourt, Michelle Kelly, Tom Postle, Luke |
| author_facet | Delcourt, Michelle Kelly, Tom Postle, Luke |
| contents | We prove that if $p \geq n^{-(q-6)/2}$, then asymptotically almost surely the binomial random $q$-uniform hypergraph $G^{(q)}(n,p)$ contains an $(n,q,2)$-Steiner system, provided $n$ satisfies the necessary divisibility conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17858 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thresholds for $(n,q,2)$-Steiner Systems via Refined Absorption Delcourt, Michelle Kelly, Tom Postle, Luke Combinatorics 05B05, 05B07, 05C80 We prove that if $p \geq n^{-(q-6)/2}$, then asymptotically almost surely the binomial random $q$-uniform hypergraph $G^{(q)}(n,p)$ contains an $(n,q,2)$-Steiner system, provided $n$ satisfies the necessary divisibility conditions. |
| title | Thresholds for $(n,q,2)$-Steiner Systems via Refined Absorption |
| topic | Combinatorics 05B05, 05B07, 05C80 |
| url | https://arxiv.org/abs/2402.17858 |