论文标题
Dyck路径粉丝的促销和生长图
Promotion and growth diagrams for fans of Dyck paths and vacillating tableaux
论文作者
论文摘要
我们从$ [n] $上的一组和弦图中构造了一组$ r $ r $ fans dyck路径（分别浮力的tableaux）长度$ n $的注入。这是通过两种不同的方式完成的，即作为促销蒸发图的填充图和Fomin生长图。我们的分析使用了这样一个事实，即dyck路径的$ r $粉丝和浮力tableaux可以看作是分别在$ b_r $和$ b_r $和$ c_r $的晶体中重量零的最高重量元素，而这又可以使用虚拟晶体对其进行分析。在Fomin生长图的水平上，虚拟化过程对应于Roby-Krattenthaler爆炸的结构。找到旋转不变的图表基础（例如和弦图）的动机之一是环状筛分现象。的确，我们使用促销行动对dyck路径的$ r $ r $ fans进行了环状筛分现象。
We construct an injection from the set of $r$-fans of Dyck paths (resp. vacillating tableaux) of length $n$ into the set of chord diagrams on $[n]$ that intertwines promotion and rotation. This is done in two different ways, namely as fillings of promotion-evacuation diagrams and in terms of Fomin growth diagrams. Our analysis uses the fact that $r$-fans of Dyck paths and vacillating tableaux can be viewed as highest weight elements of weight zero in crystals of type $B_r$ and $C_r$, respectively, which in turn can be analyzed using virtual crystals. On the level of Fomin growth diagrams, the virtualization process corresponds to the Roby-Krattenthaler blow up construction. One of the motivations for finding rotation invariant diagrammatic bases such as chord diagrams is the cyclic sieving phenomenon. Indeed, we give a cyclic sieving phenomenon on $r$-fans of Dyck paths and vacillating tableaux using the promotion action.
