论文标题
标记有序树中最深的节点
Deepest nodes in marked ordered trees
论文作者
论文摘要
研究有序的树的变化，其中每个最右边的边缘是否不会导致端子，都会被标记。 E. Deutsch等人引入了这些标记的树木，以模拟偏斜的戴克路径。我们研究了此类树木中最深的节点的数量。建立了显式生成功能，并且最深的节点的平均数量是当节点数量较大时接近$ \ frac53 $的平均数量。将其与标准有序的树木进行比较，其中最深的节点的平均数量接近$ 2 $。
A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al.\ to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches $\frac53$ when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches $2$.
