Some properties of the singular words of the Fibonacci word
European Journal of Combinatorics
A division property of the Fibonacci word
Information Processing Letters
&agr;-words and factors of characteristic sequences
Discrete Mathematics
A representation theorem of the suffixes of characteristic sequences
Discrete Applied Mathematics
Unbordered factors of the characteristic sequences of irrational numbers
Theoretical Computer Science
Locating factors of the infinite Fibonacci word
Theoretical Computer Science
Factors of characteristic words: Location and decompositions
Theoretical Computer Science
Theoretical Computer Science
Fibonacci word patterns in two-way infinite Fibonacci words
Theoretical Computer Science
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For each suffix X of a two-way infinite Fibonacci word, we consider the factorization X=u"ku"k"+"1u"k"+"2..., where k is a positive integer, and the length of the factor u"i is the ith Fibonacci number (i=k). It is called the Fibonacci factorization of X of order k. We show that in such a factorization, either all u"i are singular words, or there exists a positive integer l=k such that u"l,u"l"+"1,u"l"+"2,... are the Fibonacci words along an infinite path in the tree of Fibonacci words and the rest of the u"is are singular words. The labels of such infinite paths are determined by the D-representation of nonnegative integers.