Infinite antichains of matroids with characteristic set \(\{ p\}\) (Q5957754)
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scientific article; zbMATH DE number 1719009
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infinite antichains of matroids with characteristic set \(\{ p\}\) |
scientific article; zbMATH DE number 1719009 |
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Infinite antichains of matroids with characteristic set \(\{ p\}\) (English)
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24 August 2002
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For each prime \(p\) an infinite antichain of matroids is constructed in which each matroid is only representable over fields of chareacteristic \(p\). A fundamental tool in this construction is a canonical triple of perfect matchings of the complete graph on an even number of vertices. For \(p=2\), each of the matroids in the constructed antichain is an excluded minor for the class of matroids representable over the rationals. The authors conjecture that this also holds for all other prime characteristics.
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matroids
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characteristic sets
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infinite antichains
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