Caps and Wickets
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911262535843840 |
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| author | Führer, Jakob Solymosi, Jozsef |
| author_facet | Führer, Jakob Solymosi, Jozsef |
| contents | Let $H_n^{(3)}$ be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, {\em wicket}, is formed by three rows and two columns of a $3 \times 3$ point matrix. In this note, we give a new lower bound on the Turán number of wickets using estimates on cap sets. We also show that this problem is closely connected to important questions in additive combinatorics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Caps and Wickets Führer, Jakob Solymosi, Jozsef Combinatorics Let $H_n^{(3)}$ be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, {\em wicket}, is formed by three rows and two columns of a $3 \times 3$ point matrix. In this note, we give a new lower bound on the Turán number of wickets using estimates on cap sets. We also show that this problem is closely connected to important questions in additive combinatorics. |
| title | Caps and Wickets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.00923 |