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Published in:
2010 | OriginalPaper | Chapter
Bases of Primitive Nonpowerful Sign Patterns
Authors : Guanglong Yu, Zhengke Miao, Jinlong Shu
Published in: Combinatorial Optimization and Applications
Publisher: Springer Berlin Heidelberg
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For a square primitive nonpowerful sign pattern
A
, the base of
A
, denoted by
l
(
A
), is the least positive integer
l
such that every entry of
A
l
is #. In this paper, we consider the base set of the primitive nonpowerful sign pattern matrices. Some bounds on the bases for the sign pattern matrices with base at least
$\displaystyle \frac{3}{2}n^{2}-2n+4$
is given. Some sign pattern matrices with given bases is characterized and some “
gaps
” in the base set are shown.