论文标题
用空气口袋的堤防路径枚举
Enumeration of Dyck paths with air pockets
论文作者
论文摘要
我们介绍并研究了带有空气口袋的戴克路径的新组合类别。我们展示了带有无峰Motzkin路径的两者，该路径传递了几种模式统计，并为图案分布作为峰，回报和金字塔提供了双变量生成函数。然后，我们推断出这些模式的受欢迎程度和渐近期望，并指出金字塔的受欢迎程度与一种特殊的封闭的平滑自相传制曲线（斐波那契曲折的子集）之间的联系。进行了类似的研究，用于使用空气口袋的非降低戴克路径。
We introduce and study the new combinatorial class of Dyck paths with air pockets. We exhibit a bijection with the peakless Motzkin paths which transports several pattern statistics and give bivariate generating functions for the distribution of patterns as peaks, returns and pyramids. Then, we deduce the popularities and asymptotic expectations of these patterns and point out a link between the popularity of pyramids and a special kind of closed smooth self-overlapping curves, a subset of Fibonacci meanders. A similar study is conducted for non-decreasing Dyck paths with air pockets.
