论文标题
在泥树上的新等级分配和$ 132 $避免排列的分解
New equidistributions on plane trees and decompositions of $132$-avoiding permutations
论文作者
论文摘要
本文中，我们的主要结果是在蓝色的新等分方面和$ 132 $避免置换的排列，两个密切相关的对象。至于前者，我们发现了平面树的顶点的特征，该特征同样分布为顶点的高度。后者关注的是将$ 132 $避开$ 132 $的排列分解为子序列的四种不同的方式。我们合并表明，四个分解的子序列长度分布是相互等价的，并且有一种方法可以将四个分为两组分为两组，以使每个组都是对称的，并且一组的关节长度分布与另一组相同。讨论了一些后果。例如，我们提供了内部顶点和叶的等分分配的新完善，并提供了$ 132 $ - 避免$ 132 $的排列的新组，这些排列由Motzkin数字及其改进来计算。
Our main results in this paper are new equidistributions on plane trees and $132$-avoiding permutations, two closely related objects. As for the former, we discover a characteristic for vertices of plane trees that is equally distributed as the height for vertices. The latter is concerned with four distinct ways of decomposing a $132$-avoiding permutation into subsequences. We show combinatorially that the subsequence length distributions of the four decompositions are mutually equivalent, and there is a way to group the four into two groups such that each group is symmetric and the joint length distribution of one group is the same as that of the other. Some consequences are discussed. For instance, we provide a new refinement of the equidistribution of internal vertices and leaves, and present new sets of $132$-avoiding permutations that are counted by the Motzkin numbers and their refinements.
