The primitive Boolean matrices with the second largest scrambling index by Boolean rank

Shao, Yan Ling, and Gao, Yubin. "The primitive Boolean matrices with the second largest scrambling index by Boolean rank." Czechoslovak Mathematical Journal 64.1 (2014): 269-283. <http://eudml.org/doc/261990>.

@article{Shao2014,
abstract = {The scrambling index of an $n\times n$ primitive Boolean matrix $A$ is the smallest positive integer $k$ such that $A^k(A^\{\rm T\})^k=J$, where $A^\{\rm T\}$ denotes the transpose of $A$ and $J$ denotes the $n\times n$ all ones matrix. For an $m\times n$ Boolean matrix $M$, its Boolean rank $b(M)$ is the smallest positive integer $b$ such that $M=AB$ for some $m\times b$ Boolean matrix $A$ and $b\times n$ Boolean matrix $B$. In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an $n\times n$ primitive matrix $M$ in terms of its Boolean rank $b(M)$, and they also characterized all primitive matrices that achieve the upper bound. In this paper, we characterize primitive Boolean matrices that achieve the second largest scrambling index in terms of their Boolean rank.},
author = {Shao, Yan Ling, Gao, Yubin},
journal = {Czechoslovak Mathematical Journal},
keywords = {scrambling index; primitive matrix; Boolean rank; scrambling index; primitive matrix; Boolean rank},
language = {eng},
number = {1},
pages = {269-283},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The primitive Boolean matrices with the second largest scrambling index by Boolean rank},
url = {http://eudml.org/doc/261990},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Shao, Yan Ling
AU - Gao, Yubin
TI - The primitive Boolean matrices with the second largest scrambling index by Boolean rank
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 269
EP - 283
AB - The scrambling index of an $n\times n$ primitive Boolean matrix $A$ is the smallest positive integer $k$ such that $A^k(A^{\rm T})^k=J$, where $A^{\rm T}$ denotes the transpose of $A$ and $J$ denotes the $n\times n$ all ones matrix. For an $m\times n$ Boolean matrix $M$, its Boolean rank $b(M)$ is the smallest positive integer $b$ such that $M=AB$ for some $m\times b$ Boolean matrix $A$ and $b\times n$ Boolean matrix $B$. In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an $n\times n$ primitive matrix $M$ in terms of its Boolean rank $b(M)$, and they also characterized all primitive matrices that achieve the upper bound. In this paper, we characterize primitive Boolean matrices that achieve the second largest scrambling index in terms of their Boolean rank.
LA - eng
KW - scrambling index; primitive matrix; Boolean rank; scrambling index; primitive matrix; Boolean rank
UR - http://eudml.org/doc/261990
ER -