{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:46:22Z","timestamp":1774626382433,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\mathcal F$ be\u00a0 a set of $k$ by $k$ nonnegative matrices such that every \"long\" product of elements of $\\mathcal F$ is positive.\u00a0\u00a0 Cohen and Sellers (1982) proved that, then,\u00a0 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\u00a0 product of length $2^k-3$ over $\\mathcal F$ and they constructed one example of size $2^k-2$.\u00a0 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.<\/jats:p>","DOI":"10.37236\/5193","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T17:30:39Z","timestamp":1578677439000},"source":"Crossref","is-referenced-by-count":4,"title":["Lifespan in a Primitive Boolean Linear Dynamical System"],"prefix":"10.37236","volume":"22","author":[{"given":"Yaokun","family":"Wu","sequence":"first","affiliation":[]},{"given":"Yinfeng","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,11,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:07:55Z","timestamp":1579237675000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,27]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5193","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,27]]},"article-number":"P4.36"}}