On the independence numbers of a matroid (Q1093645)
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scientific article; zbMATH DE number 4023301
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the independence numbers of a matroid |
scientific article; zbMATH DE number 4023301 |
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On the independence numbers of a matroid (English)
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1989
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Given a finite subset E of a vector space of dimension 4. The number of k-independent subsets of E will be denoted by \(I_ k\). We prove that k \(I^ 2_ k\geq (k+1)I_{k-1}I_{k+1}+I_{k-1}I_ k\). The equality holds if and only if all 4-subsets of E are independent. We prove this relation for matroids of rank 4. In particular we prove Mason's conjecture on the independence numbers of a matroid for \(k=3\).
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log-concave sequence
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independence numbers of a matroid
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