| Multi-dimensional versions of a formula of Popoviciu |
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| 作者姓名： | Zhi-qiang XU Institute of Computational Math and Sci/Eng Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China |
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| 作者单位： | Zhi-qiang XU Institute of Computational Math and Sci/Eng Computing，Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China |
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| 摘 要： | In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s×(s 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of non-negative integer solutions of ax by = n which is given by Popoviciu in 1953.
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| 收稿时间： | 15 March 2006 |
| 修稿时间： | 11 September 2006 |
Multi-dimensional versions of a formula of Popoviciu |
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| Zhi-qiang XU Institute of Computational Math and Sci/Eng Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing ,China.Multi-dimensional versions of a formula of Popoviciu[J].Science in China(Mathematics),2007,50(2):285-291. |
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| Authors: | Zhi-qiang Xu |
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| Institution: | Institute of Computational Math and Sci/Eng Computing, Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on
multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer
solutions of s × (s + 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number
of non-negative integer solutions of ax + by = n which is given by Popoviciu in 1953.
This work was supported by the National Natural Science Foundation of China (Grant No. 10401021) |
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| Keywords: | multivariate splines discrete truncated power linear Diophantine equations |
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