关于三字母无平方单词个数的改进界
组合数学
2007-05-23 v3
摘要
本文给出了三字母无平方单词个数的改进上界与下界。上界基于长度不超过110的三字母无平方单词的枚举。下界通过构造广义Brinkhuis三元组得到。寻找此类三元组的问题本质上可归约为一个组合问题，该问题可用计算机高效处理。特别地，证明了长度为n的三字母无平方单词的个数至少以65^(n/40)的速度增长，取代了先前最佳的2^(n/17)下界。
引用
@article{arxiv.math/0105245,
title = {Improved bounds on the number of ternary square-free words},
author = {Uwe Grimm},
journal= {arXiv preprint arXiv:math/0105245},
year = {2007}
}
备注
17 pages, AMS LaTeX. Paper has been completely rewritten and comprises new results on both lower and upper bounds. The Mathematica program mentioned in the article can be downloaded at http://mcs.open.ac.uk/ugg2/wordcomb/brinkhuistriples.m