Polynomial versus Exponential Growth in Repetition-Free Binary Words

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

It is known that the number of overlap-free binary words of length n grows polynomially, while the number of cubefree binary words grows exponentially. We show that the dividing line between polynomial and exponential growth is 7/3. More precisely, there are only polynomially many binary words of length n that avoid 7/3-powers, but there are exponentially many binary words of length n that avoid (7/3+)-powers. This answers an open question of Kobayashi from 1986.
12 pages

Keywords

Combinatorics, Discrete Mathematics, 68R15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/67012

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304095
 http://arxiv.org/abs/math/0304095

Collections

arXiv