Tiling the Morse sequence

On the delta sequence of the Thue-Morse sequence

In this note, we investigate the delta sequence associated to the classical Thue-Morse sequence and prove a conjecture about the delta sequence. Further, we generalize the Thue-Morse sequence and show some results about this new sequence and its associated delta sequence. 1 Motivation and Some Definitions The Thue-Morse (TM) sequence T = (tn)n≥0 is defined as the limit of iterates φn(0), where ...

Rarified Sums of the Thue-morse Sequence

Let q be an odd number and Sq,0(n) the difference between the number of k < n, k ≡ 0 mod q, with an even binary digit sum and the corresponding number of k < n, k ≡ 0 mod q, with an odd binary digit sum. A remarkable theorem of Newman says that S3,0(n) > 0 for all n. In this paper it is proved that the same assertion holds if q is divisible by 3 or q = 4N + 1. On the other hand, it is shown tha...

An Overview of the Thue-Morse Sequence

Nonoverlap Property of the Thue-Morse Sequence

In this note, we provide a new proof for the nonoverlap property of the ThueMorse sequence using a Boolean functions approach and investigate other patterns that occur in a generalization of the Thue-Morse sequence.

Hankel determinants of the Thue-Morse sequence