[1]胡双年,李艳艳,朱玉清,等.定义在多重互素GCD封闭集上Smith矩阵行列式的整除性[J].四川师范大学学报(自然科学版),2020,43(01):45-49.[doi:10.3969/j.issn.1001-8395.2020.01.006]
 HU Shuangnian,LI Yanyan,ZHU Yuqing,et al.The Divisibility of the Determinants of the Smith Matrices on Multiple Coprime GCD-closed Sets[J].Journal of SichuanNormal University,2020,43(01):45-49.[doi:10.3969/j.issn.1001-8395.2020.01.006]
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定义在多重互素GCD封闭集上Smith矩阵行列式的整除性()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年01期
页码:
45-49
栏目:
基础理论
出版日期:
2019-12-04

文章信息/Info

Title:
The Divisibility of the Determinants of the Smith Matrices on Multiple Coprime GCD-closed Sets
文章编号:
1001-8395(2020)01-0045-05
作者:
胡双年1 李艳艳2 朱玉清1 牛玉俊1
1. 南阳理工学院 数学与统计学院, 河南 南阳 473004; 2. 南阳理工学院 电子与电气工程学院, 河南 南阳 473004
Author(s):
HU Shuangnian1 LI Yanyan2 ZHU Yuqing1 NIU Yujun1
1.School of Mathematics and Statistics, Nanyang Institute of Technology, Nanyang 473004, Henan; 2.School of Electronic and Electrical Engineering, Nanyang Institute of Technology, Nanyang 473004, Henan
关键词:
Smith矩阵 行列式 多重互素最大公因子封闭集
Keywords:
smith matrices determinant multiple coprime GCD-closed sets
分类号:
O156.1; O156.4
DOI:
10.3969/j.issn.1001-8395.2020.01.006
文献标志码:
A
摘要:
设f为算术函数,S={x1,x2,…,xn}是由n个不同的正整数构成的集合.用(f(S))=(f(xi,xj))(1≤i,j≤n)表示一个n阶方阵,其i行j列处的元素为f在xi和xj的最大公因子(xi,xj)处的取值.用(f[S])=(f[xi,xj])(1≤i,j≤
Abstract:
Let f be an arithmetic function and S={x1,…, xn} be a set ofn distinct positive integers. By (f(xi, xj))(resp.(f[xi, xj]))we denote the n×n matrix having f evaluated at the greatest common divisor (xi, xj)(resp. the least common multiple [xi, xj])of xi and xj as its (i,j)-entry, respectively. We say that S consists of multiple coprime GCD-closed sets if there is a positive integer h and h distinct GCD-closed sets S1,…, Sh with (lcm(Si), lcm(Sj))=1 for all integers i and j with 1≤i≠ j≤h such thatS can be partitioned as the union of S1,…, Sh. In this paper, we give the relationship of the determinants of Smith matrices (f(S)) and (f[S]).

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-01-31 接受日期:2018-10-25 基金项目:国家自然科学基金(11501387、U1504105)、河南省科技厅项目(182102210379)和河南省教育厅项目(17A110010) 第一作者简介: 胡双年(1982—),男,副教授,主要从事数论的研究,E-mail:hushuangnian@163.com
更新日期/Last Update: 2019-12-04