论文标题
类型$ \ tilde {\ mathbb {a}} _ n $的特殊序列的组合
Combinatorics of Exceptional Sequences of Type $\tilde{\mathbb{A}}_n$
论文作者
论文摘要
众所周知，欧几里得纪颤动的Quiver表示有无限的异常序列。在本文中，我们研究了类型$ \ tilde {\ mathbb {a}} _ n $的类型，并将其分类为有限的许多参数化家庭。我们首先在特殊集合和称为链图的组合对象之间进行两者进行两者进行两者进行两次射击。然后，我们将把这些链图视为和弦图，然后在环上弧图。使用ARC图，我们将定义特殊集合的参数化家族，并使用弧度图来表明有很多这样的家族。我们还表明，这些特殊集合的家族与小弧图的等效类别进行了培养。最后，我们使用有界派生类别的迁移组件对参数化家族提供了代数解释。
It is known that there are infinitely many exceptional sequences of quiver representations for Euclidean quivers. In this paper we study those of type $\tilde{\mathbb{A}}_n$ and classify them into finitely many parametrized families. We first give a bijection between exceptional collections and a combinatorial object known as strand diagrams. We will then realize these strand diagrams as chord diagrams and then arc diagrams on an annulus. Using arc diagrams, we will define parametrized families of exceptional collections and use arc diagrams to show that there are finitely many such families. We moreover show that these families of exceptional collections are in bijection with equivalence classes of small arc diagrams. Finally, we provide an algebraic explanation of parametrized families using the transjective component of the bounded derived category.
