English
A reasonably-sized morphism giving Abelian critical exponent less than 2
Multi angle
Auteurs : Currie, James D. (Auteur de la Conférence)
CIRM (Editeur )
68R15 - Combinatorics on words
CIRM (Editeur )
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Résumé :
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
Codes MSC : Keywords : Abelian repetition; Dejean's conjecture; critical exponent, morphic word
68R15 - Combinatorics on words
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 22/03/2024 Date de captation : 26/02/2024 Sous collection : Research talks arXiv category : Combinatorics ; Formal Languages and Automata Theory Domaine : Combinatorics Format : MP4 (.mp4) - HD Durée : 00:37:56 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-02-26_Currie.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Combinatorics on words / Combinatoire des mots - Week 5Organisateurs de la rencontre : Andrieu, Mélodie ; Ben Ramdhane, Firas ; Cassaigne, Julien ; Frid, Anna Dates : 26/02/2024 - 01/03/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3152.html
Données de citation
DOI : 10.24350/CIRM.V.20147903Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Thue choice number and the counting argument / Auteur de la Conférence Rosenfeld, Matthieu.
- [Multi angle] Around Cobham's theorem / Auteur de la Conférence Krawczyk, Elzbieta.
- [Multi angle] Algebraic automatic continued fractions in characteristic 2 / Auteur de la Conférence Hu, Yining.
- [Multi angle] String attractors of Rote sequences / Auteur de la Conférence Hendrychová, Veronika.
Bibliographie
- 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
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