Riordan 矩阵在广义 Motzkin 路计数中的应用

摘要

用 Riordan 矩阵的方法研究了具有4种步型的加权格路(广义 Motzkin 路)的计数问题，引入了一类新的计数矩阵，即广义 Motzkin 矩阵。同时给出了这类矩阵的 Riordan 表示，也得到了广义 Motzkin 路的计数公式。 Catalan 矩阵， Schr¨oder 矩阵和Motzkin矩阵都是广义Motzkin矩阵的特殊情形。%By means of Riordan arrays, the counting problems of weighted latticed paths with four types of steps (generalized Motzkin paths) are studied, and a new class of enumerative arrays, i.e., generalized Motzkin arrays, are introduced. Meanwhile, the Riordan array expressions of these arrays are given, and the counting formulas also obtained. It turns out that Catalan array, Schr¨oder array and Motzkin array are all the special cases of the generalized Motzkin arrays.