The combinatorial properties of the Fibonacci infinite word are of great interest in some aspects of mathematics and physics, such as number theory, fractal geometry, formal language, computational complexity , quasicrystals etc. In this note, we introduce the singular words of the Fibonacci infinite word and discuss their properties. We establish two… (More)
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula determined by the characteristic polynomial.