Honghai Li, College of Mathematic and Information Science, Jiangxi Normal University, Nanchang, JiangXi, 330022, P. R. China, e-mail: lhh@mail.ustc.edu.cn; Jiongsheng Li, Department of Mathematics, University of Science and Technology of China, Hefei, AnHui, 230026, P. R. China, e-mail: lijs@ustc.edu.cn
Abstract: A matrix $\Cal{A}$ whose entries come from the set $\{+,-,0\}$ is called a sign pattern matrix, or sign pattern. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, the characterization problem for some potentially nilpotent double star sign patterns is discussed. A class of double star sign patterns, denoted by ${\cal DSSP}(m,2)$, is introduced. We determine all potentially nilpotent sign patterns in ${\cal DSSP}(3,2)$ and ${\cal DSSP}(5,2)$, and prove that one sign pattern in ${\cal DSSP}(3,2)$ is potentially stable.
Keywords: sign pattern, double star, potentially nilpotent, potentially stable
Classification (MSC 2000): 05C50, 15A18
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