On skew corner-free sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913216640057344 |
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| author | Pohoata, Cosmin Zakharov, Dmitrii |
| author_facet | Pohoata, Cosmin Zakharov, Dmitrii |
| contents | We construct skew corner-free sets in $[n]^2$ of size $n^{5/4}$, thereby disproving a conjecture of Kevin Pratt. We also show that any skew corner-free set in $\mathbb{F}_{q}^{n} \times \mathbb{F}_{q}^{n}$ must have size at most $q^{(2-c)n}$, for some positive constant $c$ which depends on $q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On skew corner-free sets Pohoata, Cosmin Zakharov, Dmitrii Combinatorics We construct skew corner-free sets in $[n]^2$ of size $n^{5/4}$, thereby disproving a conjecture of Kevin Pratt. We also show that any skew corner-free set in $\mathbb{F}_{q}^{n} \times \mathbb{F}_{q}^{n}$ must have size at most $q^{(2-c)n}$, for some positive constant $c$ which depends on $q$. |
| title | On skew corner-free sets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.17507 |