FINITE REPETITION THRESHOLD FOR LARGE ALPHABETS

被引：1
|
作者：
Badkobeh, Golnaz [1 ]
Crochemore, Maxime [2 ]
Rao, Michael [3 ]
机构：
[1] Kings Coll London, London WC2R 2LS, England
[2] Univ Paris Est, F-77454 Marne La Vallee, France
[3] Univ Lyon, UCBL, ENS Lyon, LIP, Lyon, France
来源：
RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS | 2014年 / 48卷 / 04期
关键词：
Morphisms; repetitions in words; Dejean's threshold; INFINITE BINARY WORDS; FEWEST REPETITIONS; DEJEANS CONJECTURE; LARGE SQUARES; POWERS; GROWTH;
D O I：
10.1051/ita/2014017
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We investigate the finite repetition threshold for k-letter alphabets, k >= 4, that is the smallest number r for which there exists an infinite r(+)-free word containing a finite number of r-powers. We show that there exists an infinite Dejean word on a 4-letter alphabet (i.e. a word without factors of exponent more than 7/5) containing only two 7/5-powers. For a 5-letter alphabet, we show that there exists an infinite Dejean word containing only 60 5/4-powers, and we conjecture that this number can be lowered to 45. Finally we show that the finite repetition threshold for k letters is equal to the repetition threshold for k letters, for every k >= 6.
引用
收藏
页码：419 / 430
页数：12
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