Properties of Fibonacci languages Original Research Article

The Fibonacci language Fu,v is the set of all Fibonacci words, where the first word and the second word in the Fibonacci sequence are u and v, respectively. We show that the language Fu,v is context-free free. We also show that Fu,v is not dense if the word uv contains at least two distinct letters. Let wi denote the ith Fibonacci word. When considering the Fibonacci language Fa,b for two distinct letters a and b, we show that for k⩾2 and 1⩽i