Dejean's conjecture holds for N ≥ 27

James Currie; Narad Rampersad

RAIRO - Theoretical Informatics and Applications (2009)

  • Volume: 43, Issue: 4, page 775-778
  • ISSN: 0988-3754

Abstract

top
We show that Dejean's conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

How to cite

top

Currie, James, and Rampersad, Narad. "Dejean's conjecture holds for N ≥ 27." RAIRO - Theoretical Informatics and Applications 43.4 (2009): 775-778. <http://eudml.org/doc/250568>.

@article{Currie2009,
abstract = { We show that Dejean's conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible. },
author = {Currie, James, Rampersad, Narad},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Dejean's conjecture; repetitions in words; fractional exponent.; fractional exponent},
language = {eng},
month = {9},
number = {4},
pages = {775-778},
publisher = {EDP Sciences},
title = {Dejean's conjecture holds for N ≥ 27},
url = {http://eudml.org/doc/250568},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Currie, James
AU - Rampersad, Narad
TI - Dejean's conjecture holds for N ≥ 27
JO - RAIRO - Theoretical Informatics and Applications
DA - 2009/9//
PB - EDP Sciences
VL - 43
IS - 4
SP - 775
EP - 778
AB - We show that Dejean's conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.
LA - eng
KW - Dejean's conjecture; repetitions in words; fractional exponent.; fractional exponent
UR - http://eudml.org/doc/250568
ER -

References

top
  1. F.J. Brandenburg, Uniformly growing k-th powerfree homomorphisms. Theoret. Comput. Sci.23 (1983) 69–82.  Zbl0508.68051
  2. J. Brinkhuis, Non-repetitive sequences on three symbols. Quart. J. Math. Oxford34 (1983) 145–149.  Zbl0528.05004
  3. A. Carpi, On Dejean's conjecture over large alphabets. Theoret. Comput. Sci.385 (2007) 137–151.  Zbl1124.68087
  4. J.D. Currie and N. Rampersad, Dejean's conjecture holds for n ≥ 30. Theoret. Comput. Sci.410 (2009) 2885–2888.  Zbl1173.68050
  5. J.D. Currie, N. Rampersad, A proof of Dejean's conjecture, .  Zbl1215.68192URIhttp://arxiv.org/pdf/0905.1129v3
  6. F. Dejean, Sur un théorème de Thue. J. Combin. Theory Ser. A13 (1972) 90–99.  Zbl0245.20052
  7. L. Ilie, P. Ochem and J. Shallit, A generalization of repetition threshold. Theoret. Comput. Sci.345 (2005) 359–369.  Zbl1079.68082
  8. D. Krieger, On critical exponents in fixed points of non-erasing morphisms. Theoret.Comput. Sci.376 (2007) 70–88.  Zbl1111.68058
  9. M. Lothaire, Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley, Reading (1983).  Zbl0514.20045
  10. F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl.26 (1992) 199–204.  Zbl0761.68078
  11. M. Mohammad-Noori and J.D. Currie, Dejean's conjecture and Sturmian words. Eur. J. Combin.28 (2007) 876–890.  Zbl1111.68096
  12. J. Moulin Ollagnier, Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10 and 11 letters. Theoret. Comput. Sci.95 (1992) 187–205.  Zbl0745.68085
  13. J.-J. Pansiot, À propos d'une conjecture de F. Dejean sur les répétitions dans les mots. Discrete Appl. Math.7 (1984) 297–311.  Zbl0536.68072
  14. M. Rao, Last cases of Dejean's Conjecture, .  Zbl1230.68163URIhttp://www.labri.fr/perso/rao/publi/dejean.ps
  15. A. Thue, Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana7 (1906) 1–22.  
  16. A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana1 (1912) 1–67.  Zbl44.0462.01

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.