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Formal inverses of the generalized Thue-Morse sequences and variations of the Rudin-Shapiro sequence
- Source :
- Discrete Mathematics & Theoretical Computer Science, vol. 22 no. 1, Automata, Logic and Semantics (May 25, 2020) dmtcs:4954
- Publication Year :
- 2018
-
Abstract
- A formal inverse of a given automatic sequence (the sequence of coefficients of the composition inverse of its associated formal power series) is also automatic. The comparison of properties of the original sequence and its formal inverse is an interesting problem. Such an analysis has been done before for the Thue{Morse sequence. In this paper, we describe arithmetic properties of formal inverses of the generalized Thue-Morse sequences and formal inverses of two modifications of the Rudin{Shapiro sequence. In each case, we give the recurrence relations and the automaton, then we analyze the lengths of strings of consecutive identical letters as well as the frequencies of letters. We also compare the obtained results with the original sequences.<br />Comment: 20 pages
- Subjects :
- Mathematics - Number Theory
Mathematics - Combinatorics
11B83, 11B85
Subjects
Details
- Database :
- arXiv
- Journal :
- Discrete Mathematics & Theoretical Computer Science, vol. 22 no. 1, Automata, Logic and Semantics (May 25, 2020) dmtcs:4954
- Publication Type :
- Report
- Accession number :
- edsarx.1810.03533
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.23638/DMTCS-22-1-15