A reasonably-sized morphism giving Abelian critical exponent less than 2 | Vidéo | Carmin.tv

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A reasonably-sized morphism giving Abelian critical exponent less than 2

By James D. Currie

Appears in collection : Combinatorics on words / Combinatoire des mots - Week 5

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.

Information about the video

Date of recording 26/02/2024
Date of publication 22/03/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20147903
Cite this video Currie, James D. (26/02/2024). A reasonably-sized morphism giving Abelian critical exponent less than 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20147903
URL https://dx.doi.org/10.24350/CIRM.V.20147903

Domain(s)

Bibliography

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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.
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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

MSC codes

68R15 Combinatorics on words

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