Composition inverses of the variations of the Baum-Sweet sequence
Number Theory
2018-03-02 v1 Combinatorics
Abstract
Studying and comparing arithmetic properties of a given automatic sequence and the sequence of coefficients of the composition inverse of the associated formal power series (the formal inverse of that sequence) is an interesting problem. This problem was studied before for the Thue-Morse sequence. In this paper, we study arithmetic properties of the formal inverses of two sequences closely related to the well-known Baum-Sweet sequence. We give the recurrence relations for their formal inverses and we determine whether the sequences of indices at which these formal inverses take value and are regular. We also show an unexpected connection between one of the obtained sequences and the formal inverse of the Thue-Morse sequence.
Keywords
Cite
@article{arxiv.1803.00292,
title = {Composition inverses of the variations of the Baum-Sweet sequence},
author = {Łukasz Merta},
journal= {arXiv preprint arXiv:1803.00292},
year = {2018}
}
Comments
25 pages