February 9, 2024Open Access

The Tutte polynomials of genus g

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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 |B (M) |, where 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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Miezaki et al. (Fri,) studied this question.

synapsesocial.com/papers/68e7b285b6db64358770d55f https://doi.org/https://doi.org/10.48550/arxiv.2402.06845

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