Circular words and three applications: factors of the Fibonacci word, F-adic numbers, and the sequence 1, 5, 16, 45, 121, 320,..

We introduce the notion of circular words with a combinatorial constraint derived from the Zeckendorf (Fibonacci) numeration system, and get explicit group structures for these words. As a first application, we give a new result on factors of the Fibonacci word abaababaabaab . . .. Second, we present an expression of the sequence A004146 of [S] in terms of… CONTINUE READING