Let $\mathcal F$ be a set of $k$ by $k$ nonnegative matrices such that every "long" product of elements of $\mathcal F$ is positive. Cohen and Sellers (1982) proved that, then, every such product of length $2^k-2$ over $\mathcal F$ must be positive. They suggested to investigate the minimum size of such $\mathcal F$ for which there exists a non-positive product of length $2^k-3$ over $\mathcal F$ and they constructed one example of size $2^k-2$. We construct one of size $k$ and further discuss relevant basic problems in the framework of Boolean linear dynamical systems. We also formulate several primitivity properties for general discrete dynamical systems.
@article{10_37236_5193,
author = {Yaokun Wu and Yinfeng Zhu},
title = {Lifespan in a primitive {Boolean} linear dynamical system},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/5193},
zbl = {1329.05203},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5193/}
}
TY - JOUR
AU - Yaokun Wu
AU - Yinfeng Zhu
TI - Lifespan in a primitive Boolean linear dynamical system
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5193/
DO - 10.37236/5193
ID - 10_37236_5193
ER -
%0 Journal Article
%A Yaokun Wu
%A Yinfeng Zhu
%T Lifespan in a primitive Boolean linear dynamical system
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5193/
%R 10.37236/5193
%F 10_37236_5193
Yaokun Wu; Yinfeng Zhu. Lifespan in a primitive Boolean linear dynamical system. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5193
