Unions of lines in \(F^n\) (Q2827913)
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scientific article; zbMATH DE number 6642369
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unions of lines in \(F^n\) |
scientific article; zbMATH DE number 6642369 |
Statements
21 October 2016
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union of lines
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finite field
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Unions of lines in \(F^n\) (English)
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Suppose that \(d\geq 1\) is an integer, \(F\) is a finite field, \(0\leq\beta \leq 1\), and \({\mathcal L}\) is a collection of lines in \(F^n\) with \(|{\mathcal L}|\geq |F|^{2(d-1)+\beta}\). Then NEWLINE\[NEWLINE \left|\cup_{L\in{\mathcal L}}L\right|\geq c|F|^{d+\beta}, NEWLINE\]NEWLINE where \(|\cdot|\) stands for cardinality, and the positive constant \(c\) is independent on \(F\).
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