迭代RSK双射
Iterating the RSK Bijection
摘要：
我们调查的动力学著名的RSK双射置换时，迭代的各种阅读单词的录音画面。在设置的普通（行）读字，我们表明，正好有一个不动点每个分区的形状，它总是在两个步骤内从任何开始排列。我们还考虑了通过对记录表的列读字和反向读字迭代RSK而形成的修改的动力系统。我们表明，列读字给出了类似的动态的行读字。另一方面，对于反向读字，我们总是在两步之后到达2周期或不动点。事实上，我们到达一个不动点当且仅当初始表的形状是自共轭的。
英文摘要：
We investigate the dynamics of the well-known RSK bijection on permutations when iterated on various reading words of the recording tableau. In the setting of the ordinary (row) reading word, we show that there is exactly one fixed point per partition shape, and that it is always reached within two steps from any starting permutation. We also consider the modified dynamical systems formed by iterating RSK on the column reading word and the reversed reading word of the recording tableau. We show that the column reading word gives similar dynamics to the row reading word. On the other hand, for the reversed reading word, we always reach either a 2-cycle or fixed point after two steps. In fact, we reach a fixed point if and only if the shape of the initial tableau is self-conjugate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
