On Abelian repetition threshold
نویسندگان
چکیده
منابع مشابه
On the D0L Repetition Threshold
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 restricte...
متن کاملA Generalization of Repetition Threshold
Brandenburg and (implicitly) Dejean introduced the concept of repetition threshold: the smallest real number α such that there exists an infinite word over a k-letter alphabet that avoids β-powers for all β > α. We generalize this concept to include the lengths of the avoided words. We give some conjectures supported by numerical evidence and prove some of these conjectures. As a consequence of...
متن کاملRepetition Threshold for Circular Words
We find the threshold between avoidable and unavoidable repetitions in circular words over k letters for any k > 6. Namely, we show that the number CRT(k) = ⌈k/2⌉+1 ⌈k/2⌉ satisfies the following properties. For any n there exists a k-ary circular word of length n containing no repetition of exponent greater than CRT(k). On the other hand, k-ary circular words of some lengths must have a repetit...
متن کاملFinite-Repetition threshold for infinite ternary words
The exponent of a word is the ratio of its length over its smallest period. The repetitive threshold r(a) of an a-letter alphabet is the smallest rational number for which there exists an infinite word whose finite factors have exponent at most r(a). This notion was introduced in 1972 by Dejean who gave the exact values of r(a) for every alphabet size a as it has been eventually proved in 2009....
متن کاملFinite repetition threshold for large alphabets
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 2011
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita/2011127