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Entropy 2013, 15(9), 3312-3324; doi:10.3390/e15093312
Article

On the Entropy of a Two Step Random Fibonacci Substitution

Received: 8 July 2013; in revised form: 30 July 2013 / Accepted: 19 August 2013 / Published: 23 August 2013
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Abstract: We consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, a → baa and b → ab, with probability , and  → ba, with probability 1 – p for 0 < p < 1, and where the random rule is applied each time it acts on a . We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value.
Keywords: combinatorics on words; asymptotic enumeration; symbolic dynamics combinatorics on words; asymptotic enumeration; symbolic dynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Nilsson, J. On the Entropy of a Two Step Random Fibonacci Substitution. Entropy 2013, 15, 3312-3324.

AMA Style

Nilsson J. On the Entropy of a Two Step Random Fibonacci Substitution. Entropy. 2013; 15(9):3312-3324.

Chicago/Turabian Style

Nilsson, Johan. 2013. "On the Entropy of a Two Step Random Fibonacci Substitution." Entropy 15, no. 9: 3312-3324.


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