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arXiv · math/9702219

The Tutte dichromate and Whitney homology of matroids

David G. Wagner
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Abstract

We consider a specialization $Y_M(q,t)$ of the Tutte polynomial of a matroid $M$ which is inspired by analogy with the Potts model from statistical mechanics. The only information lost in this specialization is the number of loops of $M$. We show that the coefficients of $Y_M(1-p,t)$ are very simply related to the ranks of the Whitney homology groups of the opposite partial orders of the independent set complexes of the duals of the truncations of $M$. In particular, we obtain a new homological interpretation for the coefficients of the characteristic polynomial of a matroid.

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David G. Wagner. 1997-02-05. The Tutte dichromate and Whitney homology of matroids. https://arxiv.org/abs/math/9702219

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