论文标题
挂钩值tableaux的不受欢迎的算法
Uncrowding algorithm for hook-valued tableaux
论文作者
论文摘要
设定值的tableaux是与稳定的Grothendieck多项式相关的组合对象，而挂钩值tableaux与稳定的规范Grothendieck多项式相关。在本文中，我们为挂钩值tableaux定义了一种新颖的不拥挤算法。该算法“解开”钩子中的条目，并产生设定值的图表和柱状标记的增加图表。我们证明，我们的不拥挤算法与水晶算子交织在一起。还给出了一种“解开”腿上的条目而不是钩子的链接的替代性不受拥挤的算法。作为不满意的应用，我们获得了规范Grothendieck多项式的各种扩展。
Whereas set-valued tableaux are the combinatorial objects associated to stable Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. In this paper, we define a novel uncrowding algorithm for hook-valued tableaux. The algorithm "uncrowds" the entries in the arm of the hooks and yields a set-valued tableau and a column-flagged increasing tableau. We prove that our uncrowding algorithm intertwines with crystal operators. An alternative uncrowding algorithm that "uncrowds" the entries in the leg instead of the arm of the hooks is also given. As an application of uncrowding, we obtain various expansions of the canonical Grothendieck polynomials.
