{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T15:55:50Z","timestamp":1774972550627,"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>The random Fibonacci sequence is defined by $t_1 = t_2 = 1$ and $t_n = \\pm t_{n-1} + t_{n-2}$, for $n \\geq 3$, where each $\\pm$ sign is chosen at random with probability $P(+) = P(-) = \\frac{1}{2}$. Viswanath has shown that almost all random Fibonacci sequences grow exponentially at the rate $1.13198824\\ldots$. We will consider what happens to random Fibonacci sequences when we remove the randomness; specifically, we will choose coefficients which belong to the set $\\{1, -1\\}$ and form periodic cycles. By rewriting our recurrences using matrix products, we will analyze sequence growth and develop criteria based on eigenvalue, trace and order for determining whether a given sequence is bounded, grows linearly or grows exponentially. Further, we will introduce an equivalence relation on the coefficient cycles such that each equivalence class has a common growth rate, and consider the number of such classes for a given cycle length.<\/jats:p>","DOI":"10.37236\/3204","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:11:32Z","timestamp":1578687092000},"source":"Crossref","is-referenced-by-count":4,"title":["Periodic Coefficients and Random Fibonacci Sequences"],"prefix":"10.37236","volume":"20","author":[{"given":"Karyn","family":"McLellan","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,12,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:10:30Z","timestamp":1579241430000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3204","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,17]]},"article-number":"P32"}}