A vector exchange property of submodular systems (Q760438)
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scientific article; zbMATH DE number 3884186
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A vector exchange property of submodular systems |
scientific article; zbMATH DE number 3884186 |
Statements
A vector exchange property of submodular systems (English)
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1984
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The multiple basis exchange property for matroids is generalized as follows, using the sum theorem for submodular systems. If x and y are vectors in a submodular system and \(x=x_ 1+x_ 2\) then there exists \(y_ 1\), \(y_ 2\) such that \(y=y_ 1+y_ 2\) and both \(x_ 1+y_ 1\) and \(x_ 2+y_ 2\) belong to the submodular system. An integral analogue holds for integral submodular systems, and a non-negative analogue for polymatroids.
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multiple basis exchange property for matroids
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sum theorem for submodular systems
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polymatroids
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