Intertwining of Complementary Thue-Morse Factors

Abstract

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.