@MISC{Frid01overlap-freesymmetric, author = {Anna E. Frid}, title = {Overlap-Free Symmetric D0L words}, year = {2001} }

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Abstract

Introduction In his classical 1912 paper [15] (see also [3]), A. Thue gave the first example of an overlap-free infinite word, i. e., of a word which contains no subword of the form axaxa for any symbol a and word x. Thue's example is known now as the Thue-Morse word w TM = 01101001100101101001011001101001 : : :: It was rediscovered several times, can be constructed in many alternative ways and occurs in various fields of mathematics (see the survey [1]). The set of all overlap-free words was studied e. g. by Fife [8] who described all binary overlap-free infinite words and Seebold [13] who proved that the Thue-Morse word is essentially the only binary overlap-free word which is a fixed point of a morphism. Nowadays the theory of overlap-free words is a part of a more general theory of pattern avoidance [5]. J.-P. Allouche and J. Shallit [2] asked if the initial Thue's construction of an overlap-free wo