# ${\mathcal{D}}_{n,r}$ is not potentially nilpotent for $n\ge 4r-2$

Yan Ling Shao; Yubin Gao; Wei Gao

Czechoslovak Mathematical Journal (2016)

- Volume: 66, Issue: 3, page 671-679
- ISSN: 0011-4642

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topShao, Yan Ling, Gao, Yubin, and Gao, Wei. "$\mathcal {D}_{n,r}$ is not potentially nilpotent for $n \ge 4r-2$." Czechoslovak Mathematical Journal 66.3 (2016): 671-679. <http://eudml.org/doc/286814>.

@article{Shao2016,

abstract = {An $n\times n$ sign pattern $\mathcal \{A\}$ is said to be potentially nilpotent if there exists a nilpotent real matrix $B$ with the same sign pattern as $\mathcal \{A\}$. Let $\mathcal \{D\}_\{n,r\}$ be an $n\times n$ sign pattern with $2\le r \le n$ such that the superdiagonal and the $(n,n)$ entries are positive, the $(i,1)$$(i=1, \dots , r)$ and $(i,i-r+1)$$(i=r+1, \dots , n)$ entries are negative, and zeros elsewhere. We prove that for $r\ge 3$ and $n \ge 4r-2$, the sign pattern $\mathcal \{D\}_\{n,r\}$ is not potentially nilpotent, and so not spectrally arbitrary.},

author = {Shao, Yan Ling, Gao, Yubin, Gao, Wei},

journal = {Czechoslovak Mathematical Journal},

keywords = {sign pattern; potentially nilpotent pattern; spectrally arbitrary pattern},

language = {eng},

number = {3},

pages = {671-679},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {$\mathcal \{D\}_\{n,r\}$ is not potentially nilpotent for $n \ge 4r-2$},

url = {http://eudml.org/doc/286814},

volume = {66},

year = {2016},

}

TY - JOUR

AU - Shao, Yan Ling

AU - Gao, Yubin

AU - Gao, Wei

TI - $\mathcal {D}_{n,r}$ is not potentially nilpotent for $n \ge 4r-2$

JO - Czechoslovak Mathematical Journal

PY - 2016

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 66

IS - 3

SP - 671

EP - 679

AB - An $n\times n$ sign pattern $\mathcal {A}$ is said to be potentially nilpotent if there exists a nilpotent real matrix $B$ with the same sign pattern as $\mathcal {A}$. Let $\mathcal {D}_{n,r}$ be an $n\times n$ sign pattern with $2\le r \le n$ such that the superdiagonal and the $(n,n)$ entries are positive, the $(i,1)$$(i=1, \dots , r)$ and $(i,i-r+1)$$(i=r+1, \dots , n)$ entries are negative, and zeros elsewhere. We prove that for $r\ge 3$ and $n \ge 4r-2$, the sign pattern $\mathcal {D}_{n,r}$ is not potentially nilpotent, and so not spectrally arbitrary.

LA - eng

KW - sign pattern; potentially nilpotent pattern; spectrally arbitrary pattern

UR - http://eudml.org/doc/286814

ER -

## References

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