The Tutte polynomials of genus $g$
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909101724794880 |
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| author | Miezaki, Tsuyoshi Oura, Manabu Sakuma, Tadashi Shinohara, Hidehiro |
| author_facet | Miezaki, Tsuyoshi Oura, Manabu Sakuma, Tadashi Shinohara, Hidehiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Tutte polynomials of genus $g$ Miezaki, Tsuyoshi Oura, Manabu Sakuma, Tadashi Shinohara, Hidehiro Combinatorics Primary 05B35, Secondary 05C35, 94B05, 05C31 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. |
| title | The Tutte polynomials of genus $g$ |
| topic | Combinatorics Primary 05B35, Secondary 05C35, 94B05, 05C31 |
| url | https://arxiv.org/abs/2402.06845 |