Lead Researcher(s): Jason Geraldizo, Eden Delight Miro and Daisy Romeo
Status: Published
Abstract/summary: 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.