Lifespan in a primitive Boolean linear dynamical system
type: Item
instance of: scholarly article
title: Lifespan in a primitive Boolean linear dynamical system
zbMATH Open document ID: 1329.05203
author: Yaokun Wu
author: Yinfeng Zhu
published in: The Electronic Journal of Combinatorics
publication date: 2016-01-25T00:00:00Z
full work available at URL: v22i4p36
review text: Summary: Let \(\mathcal F\) be a set of \(k\) by \(k\) nonnegative matrices such that every ``long'' product of elements of \(\mathcal F\) is positive. \textit{J. E. Cohen} and \textit{P. H. Sellers} [Linear Algebra Appl. 47, 185--192 (1982; Zbl 0495.15013)] 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.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15B34
Mathematics Subject Classification ID: 37F20
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 6534967
zbMATH Keywords: Boolean lattice
zbMATH Keywords: hitting time
zbMATH Keywords: non-homogeneous matrix product
zbMATH Keywords: phase space
zbMATH Keywords: primitive index
zbMATH Keywords: Wielandt matrix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6534967