Scholarlink

<p>We analyse the structure of equivalence classes of symmetric quivers whose generating series are equal. We consider such classes constructed using the basic operation of unlinking, which increases the&#xa0;size of a&#xa0;quiver. The existence and features of such classes do not depend on a&#xa0;particular quiver but follow from the properties of unlinking. We show that such classes include sets of quivers assembled into permutohedra, and all quivers in a&#xa0;given class are determined by one quiver of the largest size, which we call a universal quiver. These findings generalise the previous ones for permutohedra graphs for knots. We illustrate our results with generic examples, as well as specialisations related to the knots–quivers correspondence.</p>

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Unlinking symmetric quivers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月17日

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  • Piotr Kucharski,
  • Hélder Larraguível,
  • Dmitry Noshchenko,
  • Piotr Sułkowski

摘要

We analyse the structure of equivalence classes of symmetric quivers whose generating series are equal. We consider such classes constructed using the basic operation of unlinking, which increases the size of a quiver. The existence and features of such classes do not depend on a particular quiver but follow from the properties of unlinking. We show that such classes include sets of quivers assembled into permutohedra, and all quivers in a given class are determined by one quiver of the largest size, which we call a universal quiver. These findings generalise the previous ones for permutohedra graphs for knots. We illustrate our results with generic examples, as well as specialisations related to the knots–quivers correspondence.