论文标题
异性行李和八面体复发
Birational Rowmotion and the Octahedron Recurrence
论文作者
论文摘要
我们使用八面体的复发来提供简化的陈述和证明，以迭代的双链产物的迭代式排行公式，首先是由Musiker和Roby描述的。使用此过程，我们表明矩形中某些链的权重在行电动机的作用下以可预测的方式移动。然后，我们定义了广义的史丹利 - 托马斯单词，其循环旋转唯一地决定了两个链的乘积上的异性行变量。我们还讨论了Rowmotion和Birational RSK之间的关系，并在此环境中给出了Greene定理的异性类似物。
We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in rectangles shift in a predictable way under the action of rowmotion. We then define generalized Stanley-Thomas words whose cyclic rotation uniquely determines birational rowmotion on the product of two chains. We also discuss the relationship between rowmotion and birational RSK and give a birational analogue of Greene's theorem in this setting.
