Matroids with different configurations and the same $\mathcal{G}$-invariant
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911977831399424 |
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| author | Bonin, Joseph E. |
| author_facet | Bonin, Joseph E. |
| contents | From the configuration of a matroid (which records the size and rank of the cyclic flats and the containments among them, but not the sets), one can compute several much-studied matroid invariants, including the Tutte polynomial and a newer, stronger invariant, the $\mathcal{G}$-invariant. To gauge how much additional information the configuration contains compared to these invariants, it is of interest to have methods for constructing matroids with different configurations but the same $\mathcal{G}$-invariant. We offer several such constructions along with tools for developing more. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_05482 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Matroids with different configurations and the same $\mathcal{G}$-invariant Bonin, Joseph E. Combinatorics From the configuration of a matroid (which records the size and rank of the cyclic flats and the containments among them, but not the sets), one can compute several much-studied matroid invariants, including the Tutte polynomial and a newer, stronger invariant, the $\mathcal{G}$-invariant. To gauge how much additional information the configuration contains compared to these invariants, it is of interest to have methods for constructing matroids with different configurations but the same $\mathcal{G}$-invariant. We offer several such constructions along with tools for developing more. |
| title | Matroids with different configurations and the same $\mathcal{G}$-invariant |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2108.05482 |