| 黄欣阳，伍红茹，马淑萍.降维法快速求解A(n,k)精确公式[J].南华大学学报(自然科学版),2008,22(1):60~64.[HUANG Xin-yang1,WU Hong-ru2,MA Shu-ping1.A Rapid Method of Getting the Accurate Formula of A(n,k) by Reduced Dimensions[J].Journal of University of South China(Science and Technology),2008,22(1):60~64.] |
| 降维法快速求解A(n,k)精确公式 |
| A Rapid Method of Getting the Accurate Formula of A(n,k) by Reduced Dimensions |
| 投稿时间：2007-09-13 |
| DOI： |
| 中文关键词: 快速解性线方程组 丢番图方程 解数 无序分拆 范德蒙行列式 |
| 英文关键词:Fast solve system of linear equations Diophantine equation number of solutions unordered integer partition Vandermonde determinant |
| 基金项目: |
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| 摘要点击次数: 906 |
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| 中文摘要: |
| A(n,k)=∑km=1∑mr=1∑[k/m]-1j=0t(k)m,r,j×nj×s(r,m)×ζnrm,ζm=e2πi/m,s(r,m)=1,gcd(r,m)=1 |
| 英文摘要: |
| Let A(n,k) be the number of nonnegative integer solutions for the Diophantine equation∑ki=1ixi=n. We can get all coefficients of the A(n,k), by solving the system of linear equations for the coefficients of the A(n,k), where, A(n,k)=∑km=1∑mr=1∑[k/m]-1j=0t(k)m,r,j×nj×s(r,m)×ζnrm,ζm=e2πi/m,s(r,m)=1,gcd(r,m)=10,其他.But this processing will cost our much time.To solve the problem, this paper has provided a new method, which reduces the dimensions of the system of linear equations, by collating coefficients of the qgi,qgc≠iin the A(n,k) when qgi=qgc≠i, the roots of the equation(1-x)(1-x2)..(1-xk)=0.Then the dimensions of the constructed system of linear equations are reduced, so improves the speed of solving the equations. |
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