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arXiv · 2211.11626

Representability of the Direct Sum of $q$-Matroids

Heide Gluesing-Luerssen·Benjamin Jany
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Abstract

While there are many parallels between matroid theory and $q$-matroid theory, most notably on the level of cryptomorphisms, there are substantial differences when it comes to the direct sum. The direct sum of $q$-matroids has been introduced in the literature only recently. In this short note we show that the direct sum of representable $q$-matroids may not be representable. It remains an open question whether representability of the direct sum can be characterized by the given $q$-matroids.

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Heide Gluesing-Luerssen, Benjamin Jany. 2023-02-22. Representability of the Direct Sum of $q$-Matroids. https://arxiv.org/abs/2211.11626

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