Connected matroids with symmetric Tutte polynomials (Q2726712)
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scientific article; zbMATH DE number 1621388
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Connected matroids with symmetric Tutte polynomials |
scientific article; zbMATH DE number 1621388 |
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11 December 2002
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matroids
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symmetric Tutte polynomials
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0.9177285
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0.9171833
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0.9127047
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0.91149336
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0.90586346
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0.9045949
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Connected matroids with symmetric Tutte polynomials (English)
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For an arbitrary matroid \({\mathcal M}\) having rank function \(r\) the rank Tutte polynomial is defined by NEWLINE\[NEWLINEt({\mathcal M}; x,y) =\sum_{X\subset E}(x-1)^{r(E)-r(X)}(y-1)^{|X|-r(X)},NEWLINE\]NEWLINE see \textit{T. Brylawski} and \textit{J. Oxley} [Encycl. Math. Appl. 40, 123-225 (1992; Zbl 0769.05026)]. From the definition we see that for the dual \({\mathcal M}^*(E)\) of \({\mathcal M}(E)\) we have \(t({\mathcal M}^*; x,y) = t({\mathcal M}; y,x).\) To answer a question of Welsh, the author constructs matroids that are not self-dual, have arbitrary high connectivity, and yet have symmetric Tutte polynomials.
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