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- W4385644446 abstract "Many important enumerative invariants of a matroid can be obtained from its Tutte polynomial, and many more are determined by two stronger invariants, the $mathcal{G}$-invariant and the configuration of the matroid. We show that the same is not true of the most basic connectivity invariants. Specifically, we show that for any positive integer $n$, there are pairs of matroids that have the same configuration (and so the same $mathcal{G}$-invariant and the same Tutte polynomial) but the difference between their Tutte connectivities exceeds $n$, and likewise for vertical connectivity and branch-width. The examples that we use to show this, which we construct using an operation that we introduce, are transversal matroids that are also positroids." @default.
- W4385644446 created "2023-08-08" @default.
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- W4385644446 date "2023-08-04" @default.
- W4385644446 modified "2023-10-16" @default.
- W4385644446 title "Connectivity gaps among matroids with the same enumerative invariants" @default.
- W4385644446 doi "https://doi.org/10.48550/arxiv.2308.02302" @default.
- W4385644446 hasPublicationYear "2023" @default.
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