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arXiv · 2406.14244

On simple matroids with a unique minimal tropical basis

Winfried Hochstättler
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Abstract

In this note we characterize tropical bases as sets of circuits that by orthogonality determine the set of cocircuits of a simple matroid. Furthermore, we show that any circuit, which itself is closed, must be contained in any tropical basis. This yields a characterization of simple matroids which have a unique minimal tropical basis, giving a solution for a problem posted in the Matroid Union Blog.

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Winfried Hochstättler. 2024-06-20. On simple matroids with a unique minimal tropical basis. https://arxiv.org/abs/2406.14244

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