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Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats
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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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Graph theoretic properties of Speyer's matroid polynomial $g_M(t)$
For graphic and cographic matroids, the derivative g'_M(-1) equals (-1)^{c(M)-1} c(M), and computational data suggests many new properties of the coefficient N2.
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