Multi-dimensional versions of a formula of Popoviciu  

作　　者：Zhi-qiang XU Institute of Computational Math and Sci/Eng Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China 

出　　处：《Science China Mathematics》2007年第2期285-291,共7页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 10401021)

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.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.

关 键 词：multivariate splines discrete truncated power linear Diophantine equations 41A15 05A15 

分 类 号：O241.6[理学—计算数学]