对称圈符号模式的潜在最终正性  

Symmetric cycle sign pattern that permits eventual positivity

作　　者：陈洋 刘月[1] CHEN Yang;LIU Yue(School of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《宁德师范学院学报(自然科学版)》2024年第4期337-342,共6页Journal of Ningde Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12171088)。

摘　　要：将符号模式潜在最终正性的研究从树符号模式延伸至圈符号模式,发现潜在最终正对称圈符号模式的非对角元允许存在负元,并且证明若对角元至少有一项为正,则对称圈符号模式是潜在最终正的当且仅当其非对角元至多有一对负元。同时刻画存在一对负元的潜在最终正对称圈符号模式。We extend the study of the potential eventual positivity of sign patterns from tree sign patterns to cycle sign patterns,find that the off-diagonal entries of potentially eventually positive symmetric cycle sign pat⁃terns allow the existence of negative entries,and prove that if at least one diagonal entry is positive,then sym⁃metric cycle sign patterns are potentially eventually positive if and only if its off-diagonal entries have at most one pair of negative entries.Our paper also characterizes the potential eventual positivity of symmetric cycle sign patterns with a pair of negative entries.

关 键 词：潜在最终正性 超模式 圈符号模式 本原矩阵 

分 类 号：O151.21[理学—数学]