| Riordan 矩阵的$(m,r,s)$-Halves |
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| 引用本文： | 杨琳,杨胜良. Riordan 矩阵的$(m,r,s)$-Halves[J]. 数学研究及应用, 2023, 43(3): 253-265 |
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| 作者姓名： | 杨琳 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 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11861045; 12101280), 甘肃省青年科技基金计划(Grant No.20JR10RA187). |
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| 摘 要： | Riordan矩阵的垂直一半和水平一半已经被许多学者分别研究过.本文给出了Riordan矩阵的$(m,r,s)$-halves的定义.利用此定义能够统一的讨论Riordan矩阵的垂直一半和水平一半.作为应用,通过对Pascal和Delannoy矩阵的$(m,r,s)$-halves的研究,可以得到了一些与Fibonacci, Pell和Jacobsthal序列相关的等式.
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| 关 键 词： | Riordan矩阵 中心系数 Pascal矩阵 Delannoy矩阵 Fibonacci数 Pell数 Jacobsthal数 |
| 收稿时间： | 2022-05-10 |
| 修稿时间： | 2022-08-22 |
On the $(m,r,s)$-Halves of a Riordan Array and Applications |
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| Lin YANG,Shengliang YANG. On the $(m,r,s)$-Halves of a Riordan Array and Applications[J]. Journal of Mathematical Research with Applications, 2023, 43(3): 253-265 |
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| Authors: | Lin YANG Shengliang YANG |
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| Affiliation: | School of Science, Lanzhou University of Technology, Gansu 730050, P. R. China |
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| Abstract: | Given a Riordan array, its vertical half and horizontal half are studied separately before. In the present paper, we introduce the $(m,r,s)$-halves of a Riordan array. This allows us to discuss the vertical half and horizontal half in a uniform context. As applications, we find several new identities involving Fibonacci, Pell and Jacobsthal sequences by applying the $(m,r,s)$-halves of Pascal and Delannoy matrices. |
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| Keywords: | Riordan array central coefficients Pascal matrix Delannoy matrix Fibonacci numbers Pell numbers Jacobsthal numbers |
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