论文标题
偏斜的戴克路径在1级没有峰值
Skew Dyck paths having no peaks at level 1
论文作者
论文摘要
偏斜的戴克路径是Dyck路径的变体，除步骤$（1,1）$和$（1，-1）$外，也允许使用Suth-West步骤$（-1，-1）$，前提是该路径不相交。通过一个红色的东南步骤代替西南步骤，我们最终以装饰的Dyck路径取代。整数序列的百科全书的序列A128723考虑了这种路径，其中禁止在1级处峰值达到峰值。我们提供了更一般的场景，即部分装饰的戴克路径，以规定的级别$ j $结束，无论是从左到右还是从右至左）（装饰的戴克路径都不对称）。该方法完全基于生成功能。
Skew Dyck paths are a variation of Dyck paths, where additionally to steps $(1,1)$ and $(1,-1)$ a south-west step $(-1,-1)$ is also allowed, provided that the path does not intersect itself. Replacing the south-west step by a red south-east step, we end up with decorated Dyck paths. Sequence A128723 of the Encyclopedia of Integer Sequences considers such paths where peaks at level 1 are forbidden. We provide a thorough analysis of a more general scenario, namely partial decorated Dyck paths, ending on a prescribed level $j$, both from left-to-right and from right-to-left (decorated Dyck paths are not symmetric). The approach is completely based on generating functions.
