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arXiv · 2606.14663

Maximal matroids and counterexamples

Denys Bulavka·Martin Tancer
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Abstract

Jackson and Tanigawa conjectured that the rigidity matroid $\mathcal{R}^d_n$ and the hyperconnectivity matroid $\mathcal{H}^d_n$ are the unique maximal matroids in the posets of $\{K_{d+2}, K_{d+2,d+2}\}$-matroids and $\{K_{d+2},K_{d+1,d+1}\}$-matroids, respectively. We disprove these conjectures by showing the existence of maximal matroids that are distinct from the proposed candidates.

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Denys Bulavka, Martin Tancer. 2026-06-12. Maximal matroids and counterexamples. https://arxiv.org/abs/2606.14663

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