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On potentially nilpotent double star sign patterns
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 489-501 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A matrix $\Cal A$ whose entries come from the set $\{+,-,0\}$ is called a {\it sign pattern matrix}, or {\it 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.
A matrix $\Cal A$ whose entries come from the set $\{+,-,0\}$ is called a {\it sign pattern matrix}, or {\it 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.
Classification : 05C50, 15A18
Keywords: sign pattern; double star; potentially nilpotent; potentially stable 
@article{CMJ_2009_59_2_a13,
     author = {Li, Honghai and Li, Jiongsheng},
     title = {On potentially nilpotent double star sign patterns},
     journal = {Czechoslovak Mathematical Journal},
     pages = {489--501},
     year = {2009},
     volume = {59},
     number = {2},
     mrnumber = {2532386},
     zbl = {1224.05303},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_2_a13/}
}
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Li, Honghai; Li, Jiongsheng. On potentially nilpotent double star sign patterns. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 489-501. http://geodesic.mathdoc.fr/item/CMJ_2009_59_2_a13/

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