排序不变非混乱
Sort-Invariant Non-Messing-Up
摘要：
一个偏序集具有非混乱性质，如果它有两个不相交的饱和链的覆盖集，使得对于偏序集的任何标签，沿着一个链集排序标签，然后沿着另一个集排序标签会产生偏序集的线性扩张。因此，两次排序一个标记的非混乱偏序集所产生的线性扩展可能与首先执行的排序无关。在这里，我们刻画了这样的排序不变标号的凸子集的圆柱。它们完全由避免一个特定的子模式决定：一个四个元素的菱形，其最小的两个标签出现在相对的点上。
英文摘要：
A poset has the non-messing-up property if it has two covering sets of disjoint saturated chains so that for any labeling of the poset, sorting the labels along one set of chains and then sorting the labels along the other set yields a linear extension of the poset. The linear extension yielded by thus twice sorting a labeled non-messing-up poset may be independent of which sort was performed first. Here we characterize such sort-invariant labelings for convex subposets of a cylinder. They are completely determined by avoidance of a particular subpattern: a diamond of four elements whose smallest two labels appear at opposite points.
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。
