Français
A reasonably-sized morphism giving Abelian critical exponent less than 2
Multi angle
Authors : Currie, James D. (Author of the conference)
CIRM (Publisher )
68R15 - Combinatorics on words
CIRM (Publisher )
Loading the player...
|
Abstract :
It is known that there are infinite words over finite alphabets with Abelian repetition threshold arbitrarily close to 1; however, the construction previously used involves huge alphabets. In this note we give a short cyclic morphism (length 13) over an 8-letter alphabet yielding an Abelian repetition threshold less than 1.8.
Keywords : Abelian repetition; Dejean's conjecture; critical exponent, morphic word
MSC Codes : Keywords : Abelian repetition; Dejean's conjecture; critical exponent, morphic word
68R15 - Combinatorics on words
|
Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 22/03/2024 Conference Date : 26/02/2024 Subseries : Research talks arXiv category : Combinatorics ; Formal Languages and Automata Theory Mathematical Area(s) : Combinatorics Format : MP4 (.mp4) - HD Video Time : 00:37:56 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-02-26_Currie.mp4 
|
Information on the Event
Event Title : Combinatorics on words / Combinatoire des mots - Week 5Event Organizers : Andrieu, Mélodie ; Ben Ramdhane, Firas ; Cassaigne, Julien ; Frid, Anna Dates : 26/02/2024 - 01/03/2024 Event Year : 2024; Event URL : https://conferences.cirm-math.fr/3152.html
Citation Data
DOI : 10.24350/CIRM.V.20147903Cite this video as: Currie, James D. (2024;). A reasonably-sized morphism giving Abelian critical exponent less than 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20147903 URI : http://dx.doi.org/10.24350/CIRM.V.20147903 |
See Also
- [Multi angle] Thue choice number and the counting argument / Author of the conference Rosenfeld, Matthieu.
- [Multi angle] Around Cobham's theorem / Author of the conference Krawczyk, Elzbieta.
- [Multi angle] Algebraic automatic continued fractions in characteristic 2 / Author of the conference Hu, Yining.
- [Multi angle] String attractors of Rote sequences / Author of the conference Hendrychová, Veronika.
Bibliography
- CURRIE, James D. et RAMPERSAD, Narad. A small morphism giving Abelian repetition threshold less than 2. arXiv preprint arXiv:2312.16665, 2023. - https://doi.org/10.48550/arXiv.2312.16665
- CASSAIGNE, Julien et CURRIE, James D. Words strongly avoiding fractional powers. European Journal of Combinatorics, 1999, vol. 20, no 8, p. 725-737. - https://doi.org/10.1006/eujc.1999.0329
- CURRIE, James D. What Is the Abelian Analogue of Dejean's Conjecture? ¹. Grammars and Automata for String Processing: From Mathematics and Computer Science to Biology, and Back, 2004, vol. 9, no Y6, p. 237. -
- CURRIE, James D. Pattern avoidance: themes and variations. Theoretical Computer Science, 2005, vol. 339, no 1, p. 7-18. - https://doi.org/10.1016/j.tcs.2005.01.004
- CURRIE, James et RAMPERSAD, Narad. A proof of Dejean's conjecture. Mathematics of computation, 2011, vol. 80, no 274, p. 1063-1070. - http://dx.doi.org/10.1090/S0025-5718-2010-02407-X
- DEJEAN, Françoise. Sur un théoreme de Thue. Journal of Combinatorial Theory, Series A, 1972, vol. 13, no 1, p. 90-99. -
- PETROVA, Elena A. et SHUR, Arseny M. Abelian repetition threshold revisited. In : International Computer Science Symposium in Russia. Cham : Springer International Publishing, 2022. p. 302-319. - http://dx.doi.org/10.1007/978-3-031-09574-0_19
- RAO, Michaël. Last cases of Dejean's conjecture. Theoretical Computer Science, 2011, vol. 412, no 27, p. 3010-3018. - https://doi.org/10.1016/j.tcs.2010.06.020
- SAMSONOV, Alexey V. et SHUR, Arseny M. On Abelian repetition threshold. RAIRO-Theoretical Informatics and Applications, 2012, vol. 46, no 1, p. 147-163. - https://doi.org/10.1051/ita/2011127
Imagette Video
