On simple matroids with a unique minimal tropical basis
Combinatorics
2024-06-21 v1
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.
Keywords
Cite
@article{arxiv.2406.14244,
title = {On simple matroids with a unique minimal tropical basis},
author = {Winfried Hochstättler},
journal= {arXiv preprint arXiv:2406.14244},
year = {2024}
}
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4 pages