Abstract
The studies of 1-Fibonacci word patterns and 0-Fibonacci word patterns were initiated by Turner (1988) [18] and Chuan (1993) [2] respectively. It is known that each proper suffix of the infinite Fibonacci word is an r -Fibonacci word pattern, r ∈ { 0 , 1 } . In this paper, we consider the suffixes of the two two-way infinite extensions G and G ′ of the infinite Fibonacci word. We obtain necessary and sufficient conditions for suffixes of G and G ′ to be r -Fibonacci word patterns. This gives us all the mechanical words with slope α = 5 − 1 2 which are r -Fibonacci word patterns. All possible r -seed words of each of them are determined. Finally, images of suffixes of G and G ′ under the action of certain Sturmian morphisms are computed.
Published Version
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