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arXiv · 2402.06845

The Tutte polynomials of genus $g$

Tsuyoshi Miezaki·Manabu Oura·Tadashi Sakuma·Hidehiro Shinohara
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Abstract

In the paper [Proceedings of the Japan Academy, Ser. A Mathematical Sciences, 95(10) 111-113], the authors introduce the concept of the Tutte polynomials of genus $g$ and announce that each matroid $M$ can be reconstructed from its Tutte polynomial of genus $|\mathcal{B}(M)|$, where $\mathcal{B}(M)$ denotes the family of bases of $M$. In that paper, we also announced that, for all $g$, there exist inequivalent matroids that have the same Tutte polynomial of genus $g$. In this paper, we prove these theorems.

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Tsuyoshi Miezaki, Manabu Oura, Tadashi Sakuma, Hidehiro Shinohara. 2024-02-10. The Tutte polynomials of genus $g$. https://arxiv.org/abs/2402.06845

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