Intertwining of Complementary Thue-Morse Factors

03/06/2022

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by   Jeffrey Shallit, et al.

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We consider the positions of occurrences of a factor x and its binary complement x in the Thue-Morse word t = 01101001⋯, and show that these occurrences are "intertwined" in essentially two different ways. Our proof method consists of stating the needed properties as a first-order logic formula φ, and then using a theorem-prover to prove φ.