论文标题
计算广义schröder路径
Counting generalized Schröder paths
论文作者
论文摘要
Schröder路径是从$（0,0）$到$（2n，0）$的晶格路径，带有步骤$（1,1）$，$（1，-1）$和$（2,0）$，从未低于$ x- $ axis。一条小的Schröder路径是一条Schröder路径，在$ x- $轴上没有$（2,0）$步骤。在本文中，分别为SchröderPaths和SmallSchröder路径给出了3变量生成函数$ r_l（x，y，z）$。作为推论，我们以统一的方式获得了根据该顺序计算的几种广义schröder路径的生成函数。
A Schröder path is a lattice path from $(0,0)$ to $(2n,0)$ with steps $(1,1)$, $(1,-1)$ and $(2,0)$ that never goes below the $x-$axis. A small Schröder path is a Schröder path with no $(2,0)$ steps on the $x-$axis. In this paper, a 3-variable generating function $R_L(x,y,z)$ is given for Schröder paths and small Schröder paths respectively. As corollaries, we obtain the generating functions for several kinds of generalized Schröder paths counted according to the order in a unified way.
