A stability theorem for lines in Galois planes of prime order (Q663468)
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scientific article; zbMATH DE number 6006627
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A stability theorem for lines in Galois planes of prime order |
scientific article; zbMATH DE number 6006627 |
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A stability theorem for lines in Galois planes of prime order (English)
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15 February 2012
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Let \(q\) be a prime number and \(B\) a subset of the projective plane \(PG(2,q)\). Suppose that \(B\) has at most \(3(q+1)/2-\beta\) points with \(\beta>0\) and that the number \(\delta\) of its \(0\)-secants is less than \((2(\beta+1)/3)^2/2\). Then the authors show that there is a line of the plane that contains at least \(q-(2\delta/(q+1))\) points of \(B\).
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finite geometry
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Galois planes
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blocking sets
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stability theorem
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