A note on the cycle structures of automorphisms of \(2\)-\((v,k,1)\) designs (Q2761061)
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scientific article; zbMATH DE number 1682923
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the cycle structures of automorphisms of \(2\)-\((v,k,1)\) designs |
scientific article; zbMATH DE number 1682923 |
Statements
17 December 2001
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\(2\)-\((v,k,1)\)-design
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automorphism
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cycle structure
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A note on the cycle structures of automorphisms of \(2\)-\((v,k,1)\) designs (English)
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For an automorphism of a \(2\)-\((v,k,1)\) design denote by \(p_n\) and \(b_n\) the number of \(n\)-cycles, considering actions on points and blocks, respectively. It is known that \(p_n=b_n\) holds in projective planes. Call a point (or a block) an \(n\)-point (or an \(n\)-block) if it is permuted by an \(n\)-cycle. The authors prove \(p_n\leq b_n\) for the case when every block containing two \(n\)-points is either an \(n\)-block or is fixed, and there are at least two such blocks.
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