Binary patterns in the Prouhet-Thue-Morse sequence

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Almeida, J (Author) FCUP; Klima, O (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE

Vol. 23

ISSN: 1462-7264

Indexing

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Other information

Authenticus ID: P-00V-E84

DOI: 10.46298/dmtcs.5460

Abstract (EN): We show that, with the exception of the words a(2)ba(2) and b(2)ab(2), all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite case). This result was previously attributed to unpublished work by D. Guaiana and may also be derived from publications of A. Shur only available in Russian. We also identify the (finitely many) finite binary patterns that appear non trivially, in the sense that they are obtained by applying an endomorphism that does not map the set of all segments of the sequence into itself.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13