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<p>While there are many parallels between matroid theory and <i>q</i>-matroid theory, most notably on the level of cryptomorphisms, there are substantial differences when it comes to the direct sum. In this short note, we show that the direct sum of representable <i>q</i>-matroids may not be representable. It remains an open question whether representability of the direct sum can be characterized by the given <i>q</i>-matroids.</p>

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Representability of the direct sum of q-matroids

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Heide Gluesing-Luerssen,
  • Benjamin Jany

摘要

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. 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.