4阶Hankel符号模式矩阵的若干研究  

Some studies on Hankel sign pattern matrices with order 4

作　　者：田岩 赵心茹 蒋思源 TIAN Yan;ZHAO Xinru;JIANG Siyuan(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2023年第2期163-168,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究青年项目(LQ2020021)。

摘　　要：主要考虑Hankel符号模式矩阵,研究4阶Hankel符号模式矩阵是否允许代数正以及要求代数正.结合组合矩阵论和图论的理论,研究零对角的4阶Hankel符号模式矩阵,分别给出零对角的4阶Hankel符号模式矩阵允许代数正以及要求代数正的等价条件.同时,给出一类允许代数正的4阶Hankel符号模式矩阵及其具体结构.Hankel sign pattern matrices were considered,whether Hankel sign pattern matrices with order 4 allow algebraic positivity and require algebraic positivity were studied.Combining the theories of combinatorial matrix theory and graph theory,zero diagonal Hankel sign pattern matrices with order 4 were studied,the equivalent conditions of the zero diagonal Hankel sign pattern matrices with order 4 that allow algebraic positivity and require algebraic positivity were given respectively.At the same time,a class of Hankel sign pattern matrices with order 4 that allow algebraic positivity and their specific structure were given.

关 键 词：Hankel符号模式矩阵 符号模式矩阵 允许代数正 要求代数正 

分 类 号：O151.21[理学—数学]