Grid-free linear hypergraphs via Cayley-Bacharach

Fuente: arXiv
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Autore principale: Pohoata, Cosmin
Natura: Preprint
Pubblicazione: 2026
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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