# On abelian repetition threshold

Alexey V. Samsonov; Arseny M. Shur

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2012)

- Volume: 46, Issue: 1, page 147-163
- ISSN: 0988-3754

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topSamsonov, Alexey V., and Shur, Arseny M.. "On abelian repetition threshold." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 46.1 (2012): 147-163. <http://eudml.org/doc/273053>.

@article{Samsonov2012,

abstract = {We study the avoidance of Abelian powers of words and consider three reasonable generalizations of the notion of Abelian power to fractional powers. Our main goal is to find an Abelian analogue of the repetition threshold, i.e., a numerical value separating k-avoidable and k-unavoidable Abelian powers for each size k of the alphabet. We prove lower bounds for the Abelian repetition threshold for large alphabets and all definitions of Abelian fractional power. We develop a method estimating the exponential growth rate of Abelian-power-free languages. Using this method, we get non-trivial lower bounds for Abelian repetition threshold for small alphabets. We suggest that some of the obtained bounds are the exact values of Abelian repetition threshold. In addition, we provide upper bounds for the growth rates of some particular Abelian-power-free languages.},

author = {Samsonov, Alexey V., Shur, Arseny M.},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {repetition threshold; formal languages; avoidable repetitions; abelian powers},

language = {eng},

number = {1},

pages = {147-163},

publisher = {EDP-Sciences},

title = {On abelian repetition threshold},

url = {http://eudml.org/doc/273053},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Samsonov, Alexey V.

AU - Shur, Arseny M.

TI - On abelian repetition threshold

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 1

SP - 147

EP - 163

AB - We study the avoidance of Abelian powers of words and consider three reasonable generalizations of the notion of Abelian power to fractional powers. Our main goal is to find an Abelian analogue of the repetition threshold, i.e., a numerical value separating k-avoidable and k-unavoidable Abelian powers for each size k of the alphabet. We prove lower bounds for the Abelian repetition threshold for large alphabets and all definitions of Abelian fractional power. We develop a method estimating the exponential growth rate of Abelian-power-free languages. Using this method, we get non-trivial lower bounds for Abelian repetition threshold for small alphabets. We suggest that some of the obtained bounds are the exact values of Abelian repetition threshold. In addition, we provide upper bounds for the growth rates of some particular Abelian-power-free languages.

LA - eng

KW - repetition threshold; formal languages; avoidable repetitions; abelian powers

UR - http://eudml.org/doc/273053

ER -

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