This investigation identifies distinct overlapping words in Fibonacci words, indicating prevalence patterns.
An overlapping word over an alphabet is a word of the form cxcxc where c is a letter and x is a finite word. We investigate the occurrence of overlapping words in the words generated by the Fibonacci substitution given by the rule a ↦ ab,b ↦ a . To do this, we identify the factors of maximal periodicities. Ultimately, we derive a formula for the number of distinct overlapping Fibonacci words as well as the formula for the number of their occurrences in Fibonacci words.
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Geraldizo et al. (2025) studied this question.
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