论文标题
骑士通往加泰罗尼亚人数的道路
Knight's paths towards Catalan numbers
论文作者
论文摘要
我们为给定尺寸的部分骑士的路径提供了枚举结果。我们从代数上证明，在$ x $轴上结尾的曲折骑士的路径被广义的加泰罗尼亚数字列举了，我们给出了具有给定长度的无峰的Motzkin路径的建设性两者。在列举了给定长度的部分骑士的路径之后，我们证明了锯齿形骑士在$ x $轴上的特定长度的路径被加泰罗尼亚数字计数。最后，我们提供具有给定长度的Dyck路径的建设性培养。
We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the $x$-axis are enumerated by the generalized Catalan numbers, and we give a constructive bijection with peakless Motzkin paths of a given length. After enumerating partial knight's paths of a given length, we prove that zigzag knight's paths of a given length ending on the $x$-axis are counted by the Catalan numbers. Finally, we give a constructive bijection with Dyck paths of a given length.
