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arXiv · 1407.6666

Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats

Jens Niklas Eberhardt
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Abstract

We show how the Tutte polynomial of a matroid $M$ can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats. The results imply that the Tutte polynomial of $M$ is already determined by the abstract lattice of its cyclic flats together with their cardinalities and ranks. They furthermore generalize a similiar statement for perfect matroid designs due to Mphako and help to understand families of matroids with identical Tutte polynomial as constructed by Ken Shoda.

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BibTeXRIS

Jens Niklas Eberhardt. 2014-09-25. Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats. https://arxiv.org/abs/1407.6666

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