10.46298/dmtcs.5460
https://dmtcs.episciences.org/5460
Almeida, Jorge
Jorge
Almeida
Klíma, Ondřej
Ondřej
Klíma
Binary patterns in the Prouhet-Thue-Morse sequence
We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, 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 This result was previously attributed to unpublished work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.
episciences.org
Mathematics - Combinatorics
Primary: 68R15, Secondary: 11B85, 20M05, 20M35, 37B10
2021-08-02
2021-08-30
2021-08-30
eng
journal article
arXiv:1904.07137
10.48550/arXiv.1904.07137
1365-8050
https://dmtcs.episciences.org/5460/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
vol. 23, no. 3
Automata, Logic and Semantics
Researchers
Students