Polynomial versus Exponential Growth in Repetition-Free Binary Words
组合数学
2007-05-23 v1 离散数学
摘要
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.
引用
@article{arxiv.math/0304095,
title = {Polynomial versus Exponential Growth in Repetition-Free Binary Words},
author = {Juhani Karhumaki and Jeffrey Shallit},
journal= {arXiv preprint arXiv:math/0304095},
year = {2007}
}
备注
12 pages