Topological Semi-Mixing of Random n-bonacci Substitutions

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Conference Proceeding

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We consider shift spaces generated by maps, called random substitutions, that send a letter from a finite alphabet to a finite collection of words over the same alphabet. Specifically, we study the dynamics of the shift spaces generated by the family of random n-bonacci substitutions, which is a generalization of the famous Fibonacci substitution. Using a numeration system derived from a sequence of lengths, we show that, although such shift spaces are known to be non-mixing, they satisfy a weaker condition called semi-mixing.