论文标题
堆栈与连续的散布堆叠堆栈
Stack-Sorting with Consecutive-Pattern-Avoiding Stacks
论文作者
论文摘要
我们介绍了连续的避免Pattern的堆栈堆栈映射$ \ text {sc}_σ$，这是West的堆栈分类地图$ s $的天然概括，以及Cerbai，Claebai，Claesson，Claesson，claesson和Ferrerrari和Ferrerari和Ferrerari和Ferrerari最近推出的古典Pattern-Pattern-davoidn-over-pattern-parter-patern-of-stack-nater类似物。我们表征了$ \ text {stort}（\ text {sc}_σ）$的图案$σ$，这是可通过映射$ s $ s \ circ \ circ \ circ \ text {sc}_σ$排序的一组排列的$ $σ\ in \ {123,132,321 \} $。我们还从动力学的角度研究了映射$ \ text {sc}_σ$，表征了$ \ text {sc}_σ$的定期点，用于s_3 $中的所有$σ\和计算$ \ max_ {π{π{π\ in s_n} in s_n}中$σ\ in \ {132,213,231,312 \} $。此外，我们表征了避免经典 - 图平底入的堆栈分类地图$ s_ {132} $的定期点，并且我们表明，将$ s_ {132} $的最大迭代次数发送到$ s_n $中需要$ s_n $中的置换额为$ n-1 $。该论文以许多开放的问题和猜想结尾。
We introduce consecutive-pattern-avoiding stack-sorting maps $\text{SC}_σ$, which are natural generalizations of West's stack-sorting map $s$ and natural analogues of the classical-pattern-avoiding stack-sorting maps $s_σ$ recently introduced by Cerbai, Claesson, and Ferrari. We characterize the patterns $σ$ such that $\text{Sort}(\text{SC}_σ)$, the set of permutations that are sortable via the map $s\circ\text{SC}_σ$, is a permutation class, and we enumerate the sets $\text{Sort}(\text{SC}_σ)$ for $σ\in\{123,132,321\}$. We also study the maps $\text{SC}_σ$ from a dynamical point of view, characterizing the periodic points of $\text{SC}_σ$ for all $σ\in S_3$ and computing $\max_{π\in S_n}|\text{SC}_σ^{-1}(π)|$ for all $σ\in\{132,213,231,312\}$. In addition, we characterize the periodic points of the classical-pattern-avoiding stack-sorting map $s_{132}$, and we show that the maximum number of iterations of $s_{132}$ needed to send a permutation in $S_n$ to a periodic point is $n-1$. The paper ends with numerous open problems and conjectures.
