On the D0L Repetition Threshold

Ilya Goldstein

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 44, Issue: 3, page 281-292
  • ISSN: 0988-3754

Abstract

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The repetition threshold is a measure of the extent to which there need to be consecutive (partial) repetitions of finite words within infinite words over alphabets of various sizes. Dejean's Conjecture, which has been recently proven, provides this threshold for all alphabet sizes. Motivated by a question of Krieger, we deal here with the analogous threshold when the infinite word is restricted to be a D0L word. Our main result is that, asymptotically, this threshold does not exceed the unrestricted threshold by more than a little.

How to cite

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Goldstein, Ilya. "On the D0L Repetition Threshold." RAIRO - Theoretical Informatics and Applications 44.3 (2010): 281-292. <http://eudml.org/doc/250786>.

@article{Goldstein2010,
abstract = { The repetition threshold is a measure of the extent to which there need to be consecutive (partial) repetitions of finite words within infinite words over alphabets of various sizes. Dejean's Conjecture, which has been recently proven, provides this threshold for all alphabet sizes. Motivated by a question of Krieger, we deal here with the analogous threshold when the infinite word is restricted to be a D0L word. Our main result is that, asymptotically, this threshold does not exceed the unrestricted threshold by more than a little. },
author = {Goldstein, Ilya},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {finite words; infinite words over alphabets of various sizes},
language = {eng},
month = {10},
number = {3},
pages = {281-292},
publisher = {EDP Sciences},
title = {On the D0L Repetition Threshold},
url = {http://eudml.org/doc/250786},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Goldstein, Ilya
TI - On the D0L Repetition Threshold
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/10//
PB - EDP Sciences
VL - 44
IS - 3
SP - 281
EP - 292
AB - The repetition threshold is a measure of the extent to which there need to be consecutive (partial) repetitions of finite words within infinite words over alphabets of various sizes. Dejean's Conjecture, which has been recently proven, provides this threshold for all alphabet sizes. Motivated by a question of Krieger, we deal here with the analogous threshold when the infinite word is restricted to be a D0L word. Our main result is that, asymptotically, this threshold does not exceed the unrestricted threshold by more than a little.
LA - eng
KW - finite words; infinite words over alphabets of various sizes
UR - http://eudml.org/doc/250786
ER -

References

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