A Note On -Rauzy Graphs for the Infinite Fibonacci Word
Abstract
The -Rauzy graph of order k for any infinite word is a directed graph in which an arc (v1,v2) is formed if the concatenation of the word v1 and the suffix of v2 of length k- is a subword of the infinite word. In this paper, we consider one of the important aperiodic recurrent words, the infinite Fibonacci word for discussion. We prove a few basic properties of the -Rauzy graph of the infinite Fibonacci word. We also prove that the -Rauzy graphs for the infinite Fibonacci word are strongly connected.
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