On the number of transversal matroids (Q1085162)
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scientific article; zbMATH DE number 3981185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of transversal matroids |
scientific article; zbMATH DE number 3981185 |
Statements
On the number of transversal matroids (English)
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1986
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As was previously shown by \textit{D. J. A. Welsh} [J. Comb. Theory 6, 313- 316 (1969; Zbl 0167.017)], the number of all non-isomorphic transversal matroids \(T_ n\) on an arbitrary n-set \(S_ n\) satisfies the inequality \(T_ n\geq 2^ n\). In the paper under review, the author improves this result proving that \(T_ n\geq 2^ n+n^ 2-7n\) for \(n>7\).
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