Grid-free linear hypergraphs via Cayley-Bacharach
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910023623376896 |
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| author | Pohoata, Cosmin |
| author_facet | Pohoata, Cosmin |
| contents | We give a new construction showing that for every $r\ge 3$, there exists an $r$-uniform linear hypergraph on $n$ vertices with $Θ_r(n^2)$ edges and no copy of the $r\times r$ grid. This complements the works of Füredi--Ruszinkó, Glock--Joos--Kim--Kühn--Lichev, Delcourt--Postle for $r \geq 4$, as well as the subsequent constructions of Gishboliner--Shapira and Solymosi for the case $r=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14716 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grid-free linear hypergraphs via Cayley-Bacharach Pohoata, Cosmin Combinatorics Algebraic Geometry We give a new construction showing that for every $r\ge 3$, there exists an $r$-uniform linear hypergraph on $n$ vertices with $Θ_r(n^2)$ edges and no copy of the $r\times r$ grid. This complements the works of Füredi--Ruszinkó, Glock--Joos--Kim--Kühn--Lichev, Delcourt--Postle for $r \geq 4$, as well as the subsequent constructions of Gishboliner--Shapira and Solymosi for the case $r=3$. |
| title | Grid-free linear hypergraphs via Cayley-Bacharach |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2602.14716 |