四川大学学报（自然科学版）Issue(1)：6-10,5.DOI:10.3969/j.issn.0490-6756.2015.01.002
定义在两个拟互素因子链上与算术函数相关联矩阵的行列式
Determinants of matrices associated with arithmetic functions on two quasi-coprime divisor chains
摘要
Abstract
For any integers x and y ,we use (x,y)([x,y])to denote the greatest common divisor (the least common multiple)ofxandy .Letfbe an arithmetic function andS={x1,…,xn}be a set ofndis-tinct positive integers.By (f(S))= (f(xi,xj))((f[S])= (f[xi,xj])),we denote the n×n matrix having f evaluated at (xi,xj )([xi,xj ])as its i,j-entry.The set S is called a divisor chain if there is a permutationσof {1,2,…,n}such that xσ(1)|…|xσ(n).The set S is called two quasi-coprime divisor chains if S can be partitioned as S=SI ∪S2 with all Si(1 ≤i≤2)being divisor chains and (max (S1 ), max (S2 ))=gcd (S).In this paper ,we give the formulae for the determinants of the matrices (f(S)) and (f[S])on two quasi-coprime divisor chains.关键词
算术函数/矩阵/行列式Key words
Arithmetic function/Matrix/Determinant分类
数理科学引用本文复制引用
胡双年,陈龙,谭千蓉..定义在两个拟互素因子链上与算术函数相关联矩阵的行列式[J].四川大学学报（自然科学版）,2015,(1):6-10,5.基金项目
攀枝花学院校级一般项目(2013YB10) （2013YB10）
四川省应用基础研究计划项目(2013JY0125) （2013JY0125）
攀技花学院院级项目(Y2014-04) （Y2014-04）
