论文标题
RSK Tableaux和完全交换排列的弱顺序
RSK tableaux and the weak order on fully commutative permutations
论文作者
论文摘要
对于每个完全交换的置换，我们构建了一个“布尔核心”，这是在正确的弱顺序下理想的主要秩序中最大的布尔置换。我们将一组完全交换的排列划分为最近定义的拥挤和不受欢迎的元素，其区别是他们的RSK插入tableaux是否满足了稀疏条件。我们表明，当它与Boolean Core共享RSK插入图表时，完全交通量的元素完全不受欢迎。我们介绍了正确的弱点的动态，这些动力在完全交换的排列中，对它们从不拥挤的人群变为拥挤时特别感兴趣。特别是，我们使用连续的置换模式和下降来表征正确的弱顺序下的最小拥挤元素。
For each fully commutative permutation, we construct a "boolean core," which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a sparsity condition. We show that a fully commutative element is uncrowded exactly when it shares the RSK insertion tableau with its boolean core. We present the dynamics of the right weak order on fully commutative permutations, with particular interest in when they change from uncrowded to crowded. In particular, we use consecutive permutation patterns and descents to characterize the minimal crowded elements under the right weak order.
