Summary: We consider a class of binary sequences that generalize the Thue-Morse sequence. In particular, we investigate the occurrences of palindromes in such sequences. We also introduce the notion of the first difference of a binary sequence and characterize first differences of our class of Thue-Morse type sequences. Finally, we define the concept of a "change sequence" of a given binary sequence, a sequence which encodes the positions at which a binary sequence changes values. We characterize the change sequences corresponding to our class of Thue-Morse type sequences.

11B85, 68R15

thue-Morse, binary sequence, first difference, palindrome, skew-palindrome, quasi-palindrome, change sequence, cross product, block product, Toeplitz morphism