Near optimal thresholds for existence of dilated configurations in $\mathbb{F}_q^d$
| Autor: | Bhowmik, Pablo, Rakhmonov, Firdavs |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $E\subset\mathbb{F}_q^d$ and $\lVert \cdot \rVert:\mathbb{F}_q^d\to \mathbb{F}_q$ defined as $\lVert \alpha\rVert:= \alpha_1^2+\dots+\alpha_d^2$ if $\alpha=(\alpha_1,\dots,\alpha_d)\in \mathbb{F}_q^d$, where $\mathbb{F}_q^d$ is the $d$-dimensional vector space over the finite field $\mathbb{F}_q$ with $q$ elements. Let $k\geq 1$ and $A$ is a nonempty subset of $\{(i,j):1\leq i |
| Databáze: | arXiv |
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