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arXiv · 2108.05482

Matroids with different configurations and the same $\mathcal{G}$-invariant

Joseph E. Bonin
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Abstract

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.

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Joseph E. Bonin. 2021-08-12. Matroids with different configurations and the same $\mathcal{G}$-invariant. https://doi.org/10.1016/j.jcta.2022.105637

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