# The critical exponent of the Arshon words

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 44, Issue: 1, page 139-150
- ISSN: 0988-3754

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topKrieger, Dalia. "The critical exponent of the Arshon words." RAIRO - Theoretical Informatics and Applications 44.1 (2010): 139-150. <http://eudml.org/doc/250792>.

@article{Krieger2010,

abstract = {
Generalizing the results of Thue (for n = 2) [Norske Vid. Selsk. Skr. Mat. Nat. Kl. 1 (1912) 1–67] and of Klepinin and Sukhanov (for n = 3) [Discrete Appl. Math. 114 (2001) 155–169], we prove
that for all n ≥ 2, the critical exponent of the Arshon word of order n is given by (3n–2)/(2n–2), and this exponent is attained at position 1.
},

author = {Krieger, Dalia},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Arshon words; critical exponent.; critical exponent},

language = {eng},

month = {2},

number = {1},

pages = {139-150},

publisher = {EDP Sciences},

title = {The critical exponent of the Arshon words},

url = {http://eudml.org/doc/250792},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Krieger, Dalia

TI - The critical exponent of the Arshon words

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/2//

PB - EDP Sciences

VL - 44

IS - 1

SP - 139

EP - 150

AB -
Generalizing the results of Thue (for n = 2) [Norske Vid. Selsk. Skr. Mat. Nat. Kl. 1 (1912) 1–67] and of Klepinin and Sukhanov (for n = 3) [Discrete Appl. Math. 114 (2001) 155–169], we prove
that for all n ≥ 2, the critical exponent of the Arshon word of order n is given by (3n–2)/(2n–2), and this exponent is attained at position 1.

LA - eng

KW - Arshon words; critical exponent.; critical exponent

UR - http://eudml.org/doc/250792

ER -

## References

top- S.E. Arshon, A proof of the existence of infinite asymmetric sequences on n symbols. Matematicheskoe Prosveshchenie (Mathematical Education)2 (1935) 24–33 (in Russian). Available electronically at . URIhttp://ilib.mccme.ru/djvu/mp1/mp1-2.htm
- S.E. Arshon, A proof of the existence of infinite asymmetric sequences on n symbols. Mat. Sb.2 (1937) 769–779 (in Russian, with French abstract).
- J. Berstel, Mots sans carré et morphismes itérés. Discrete Math.29 (1979) 235–244. Zbl0444.20050
- J. Berstel, Axel Thue's papers on repetitions in words: a translation. Publications du Laboratoire de Combinatoire et d'Informatique Mathématique 20, Université du Québec à Montréal (1995).
- J.D. Currie, No iterated morphism generates any Arshon sequence of odd order. Discrete Math.259 (2002) 277–283. Zbl1011.68069
- S. Kitaev, Symbolic sequences, crucial words and iterations of a morphism. Ph.D. thesis, Göteborg, Sweden (2000).
- S. Kitaev, There are no iterative morphisms that define the Arshon sequence and the σ-sequence. J. Autom. Lang. Comb.8 (2003) 43–50. Zbl1064.68053
- A.V. Klepinin and E.V. Sukhanov, On combinatorial properties of the Arshon sequence. Discrete Appl. Math.114 (2001) 155–169. Zbl0995.68506
- P. Séébold, About some overlap-free morphisms on a n-letter alphabet. J. Autom. Lang. Comb.7 (2002) 579–597. Zbl1095.68090
- P. Séébold, On some generalizations of the Thue–Morse morphism. Theoret. Comput. Sci.292 (2003) 283–298. Zbl1064.68079
- A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. Mat. Nat. Kl.1 (1912) 1–67. Zbl44.0462.01
- N.Ya. Vilenkin, Formulas on cardboard. Priroda6 (1991) 95–104 (in Russian). English summary available at , review no. MR1143732. URIhttp://www.ams.org/mathscinet/index.html

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