论文标题
红色尺寸的码头
Red sizes of quivers
论文作者
论文摘要
在本文中，我们将扩展与群集代数相关的码头的最大绿色和红色序列的概念。已经研究了与Fomin和Zelevinsky的群集代数有关的各种应用的存在。艾哈迈德（Ahmad）和李（Li）考虑了颤抖的数值度量，即箭过接收称为红色数字的最大绿色序列。在本文中，我们将此概念概括为我们称之为无限制的红色数字，这些红色数字与红色序列有关。除了建立这个更一般的框架外，我们还完全确定了所有有限突变式码头的红数和无限制的红数。此外，我们总体上对红色数字和不受限制的红色数字的可能值进行了猜想。
In this article, we will expand on the notions of maximal green and reddening sequences for quivers associated to cluster algebras. The existence of these sequences has been studied for a variety of applications related to Fomin and Zelevinsky's cluster algebras. Ahmad and Li considered a numerical measure of how close a quiver is to admitting a maximal green sequence called a red number. In this paper we generalized this notion to what we call unrestricted red numbers which are related to reddening sequences. In addition to establishing this more general framework we completely determine the red numbers and unrestricted red numbers for all finite mutation type quivers. Furthermore, we give conjectures on the possible values of red numbers and unrestricted red numbers in general.
