| Riordan 矩阵在广义 Motzkin 路计数中的应用 |
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| 引用本文： | 王丽娟,杨胜良. Riordan 矩阵在广义 Motzkin 路计数中的应用[J]. 纯粹数学与应用数学, 2016, 32(2): 160-168. DOI: 10.3969/j.issn.1008-5513.2016.02.007 |
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| 作者姓名： | 王丽娟 杨胜良 |
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| 作者单位： | 兰州理工大学理学院,甘肃 兰州,730050;兰州理工大学理学院,甘肃 兰州,730050 |
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| 基金项目： | 国家自然科学基金(11561044) |
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| 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,Schrder矩阵和Motzkin矩阵都是广义Motzkin矩阵的特殊情形.
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| 关 键 词： | Riordan矩阵 格路 Catalan矩阵 Schr¨oder矩阵 Motzkin矩阵 |
The application of Riordan arrays in counting generalized Motzkin paths |
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| Wang Lijuan,Yang Shengliang. The application of Riordan arrays in counting generalized Motzkin paths[J]. Pure and Applied Mathematics, 2016, 32(2): 160-168. DOI: 10.3969/j.issn.1008-5513.2016.02.007 |
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| Authors: | Wang Lijuan Yang Shengliang |
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| Abstract: | 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. |
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| Keywords: | Riordan array latticed path Catalan array Schr¨oder array Motzkin array |
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