Weak maps and the Tutte Polynomial
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916804567236608 |
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| author | Cho, Christine Oxley, James |
| author_facet | Cho, Christine Oxley, James |
| contents | Let $M$ and $N$ be matroids such that $N$ is the image of $M$ under a rank-preserving weak map. Generalizing results of Lucas, we prove that, for $x$ and $y$ positive, $T(M;x,y)\geq T(N;x,y)$ if and only if $x+y\geq xy$ or $M\cong N$. We give a number of consequences of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak maps and the Tutte Polynomial Cho, Christine Oxley, James Combinatorics Let $M$ and $N$ be matroids such that $N$ is the image of $M$ under a rank-preserving weak map. Generalizing results of Lucas, we prove that, for $x$ and $y$ positive, $T(M;x,y)\geq T(N;x,y)$ if and only if $x+y\geq xy$ or $M\cong N$. We give a number of consequences of this result. |
| title | Weak maps and the Tutte Polynomial |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.15606 |