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On potentially nilpotent double star sign patterns

Authors:	Honghai Li Jiongsheng Li

Institution:	(1) College of Mathematic and Information Science, Jiangxi Normal University, Nanchang, JiangXi, 330022, P.R.China;(2) Department of Mathematics, University of Science and Technology of China, Hefei, AnHui, 230026, P.R.China

Abstract:	A matrix 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 $\mathcal{D}\mathcal{S}\mathcal{S}\mathcal{P}$ (m, 2), is introduced. We determine all potentially nilpotent sign patterns in $\mathcal{D}\mathcal{S}\mathcal{S}\mathcal{P}$ (3, 2) and $\mathcal{D}\mathcal{S}\mathcal{S}\mathcal{P}$ (5, 2), and prove that one sign pattern in $\mathcal{D}\mathcal{S}\mathcal{S}\mathcal{P}$ (3, 2) is potentially stable. Supported by youth scientific funds of the Education Department of Jiangxi Province (No. GJJ09460), Natural Science Foundation of Jiangxi Normal University (No.2058), National Natural Science Foundation of China (No.10601001).

Keywords:	sign pattern double star potentially nilpotent potentially stable
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