论文标题
在Dyck路径扩展公式上的等级2群集变量
On Dyck Path Expansion Formulas for Rank 2 Cluster Variables
论文作者
论文摘要
在本文中，我们简化和推广公式，以扩大等级2群集变量的扩展。特别是，我们证明了Lee和Schiffler引入的彩色Dyck子Paths框架的等效但更简单的描述。然后，我们证明了由Feiyang Lin构成的猜测的猜想，这是有色戴克亚构件的集合和兼容对，李，李和Zelevinsky引入的对象，以研究贪婪的基础。我们将此两者与鲁佩尔的膨胀公式一起用于量子贪婪的基础元素，该元素总计兼容对，以提供Lee和Schiffler的有色Dyck Subpaths公式的量子概括。
In this paper, we simplify and generalize formulas for the expansion of rank 2 cluster variables. In particular, we prove an equivalent, but simpler, description of the colored Dyck subpaths framework introduced by Lee and Schiffler. We then prove the conjectured bijectivity of a map constructed by Feiyang Lin between collections of colored Dyck subpaths and compatible pairs, objects introduced by Lee, Li, and Zelevinsky to study the greedy basis. We use this bijection along with Rupel's expansion formula for quantum greedy basis elements, which sums over compatible pairs, to provide a quantum generalization of Lee and Schiffler's colored Dyck subpaths formula.
