The Number of Fractional Powers in the Fibonacci Word

Abstract

The Fibonacci word is the fixed point beginning with the letter $a$ of morphism $\sigma (a)=ab$, $\sigma (b)=a$ defined over the alphabet $\{a,b\}$. In this paper, we get explicit expression of the number of distinct fractional powers in each factor of the Fibonacci word.

19 pages, 9 figures