On potentially nilpotent double star sign patterns

Li, Honghai, and Li, Jiongsheng. "On potentially nilpotent double star sign patterns." Czechoslovak Mathematical Journal 59.2 (2009): 489-501. <http://eudml.org/doc/37936>.

@article{Li2009,
abstract = {A matrix $\mathcal \{A\}$ whose entries come from the set $\lbrace +,-,0\rbrace $ 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 $\{\mathcal \{D\}SSP\}(m,2)$, is introduced. We determine all potentially nilpotent sign patterns in $\{\mathcal \{D\}SSP\}(3,2)$ and $\{\mathcal \{D\}SSP\}(5,2)$, and prove that one sign pattern in $\{\mathcal \{D\}SSP\}(3,2)$ is potentially stable.},
author = {Li, Honghai, Li, Jiongsheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {sign pattern; double star; potentially nilpotent; potentially stable; sign pattern; double star; potentially nilpotent; potentially stable},
language = {eng},
number = {2},
pages = {489-501},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On potentially nilpotent double star sign patterns},
url = {http://eudml.org/doc/37936},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Li, Honghai
AU - Li, Jiongsheng
TI - On potentially nilpotent double star sign patterns
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 489
EP - 501
AB - A matrix $\mathcal {A}$ whose entries come from the set $\lbrace +,-,0\rbrace $ 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 ${\mathcal {D}SSP}(m,2)$, is introduced. We determine all potentially nilpotent sign patterns in ${\mathcal {D}SSP}(3,2)$ and ${\mathcal {D}SSP}(5,2)$, and prove that one sign pattern in ${\mathcal {D}SSP}(3,2)$ is potentially stable.
LA - eng
KW - sign pattern; double star; potentially nilpotent; potentially stable; sign pattern; double star; potentially nilpotent; potentially stable
UR - http://eudml.org/doc/37936
ER -