Involutions of connected binary matroids (Q2703020)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Involutions of connected binary matroids |
scientific article |
Statements
21 January 2002
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binary matroid
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hyperplane
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connected matroid
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Involutions of connected binary matroids (English)
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It is shown that if an involution \(\phi\) is an automorphism of a connected binary matroid \(M\) then there is a hyperplane of \(M\) that is invariant under \(\phi\), and also that both the assumptions that \(M\) is binary and connected are necessary for this result to hold. More generally, it is also shown that if \(M\) is in addition \(2k\)-connected and has at least \(4k-2\) elements with \(k \geq 1\), then there are at least \(k\) invariant hyperplanes of \(M\).
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