Statistics on Dyck Paths
Statistics on Dyck Paths
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发表时间：
2006
影响因子：
0.5
通讯作者：
T. Mansour
中科院分区：
文献类型：
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作者：
T. Mansour
本文考虑了Dyck路集合上的几个统计量。根据长度和各种其他参数的戴克路径的枚举已经在几篇论文中进行了研究。然而，统计“未成年人数量”只是最近才被考虑。我们推广了这个统计量，并根据统计量\number of uu ™ udu's”（\number of udud ™ udu's”）推导出长度为2n的Dyck路径数的显式公式。因此，我们得到了几个已知的结果，以及许多新的结果。
In this paper we consider several statistics on the set of Dyck paths. Enumeration of Dyck paths according to length and various other parameters has been studied in several papers. However, the statistic \number of udu’s" has been considered only recently. We generalize this statistic and derive an explicit formula for the number of Dyck paths of length 2n according to the statistic \number of uu ¢ ¢ ¢ udu’s" (\number of udud ¢ ¢ ¢ udu’s"). As a consequence, we derive several known results, as well as many new results.