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Infinite Sets of Square-Free omega-words Derived from the Prouhet-Thue-Morse Sequence
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Organization: | University of California, Santa Cruz |
Organization: | Rovaniemi Polytechnic |
Department: | School of Technology |
Organization: | Carnegie Mellon University |
Department: | School of Computer Science |
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2004 International Mathematica Symposium
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Banff, Canada
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We describe a method to generate an infinite set of unique square-free omega-words from the (Prouhet)-Thue-Morse sequence on a four letter alphabet. This result is a generalization of the method introduced by Axel Thue in 1912 for constructing a square-free omega-word over four (and then over three) letters from the Thue-Morse sequence. The new method has been further generalized to produce infinite sets of square-free omega-words on larger alphabets. We present a method for constructing a new square-free omega-word over three letters from an element of the infinite set of square-free omega-words over six letters that results from the generalization described above.
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Prouhet-Thue-Morse Sequence, Thue-Morse sequence, omega-words
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