There are More Than 2**(n/17) n-Letter Ternary Square-Free Words

Doron Zeilberger

There are More Than 2**(n/17) n-Letter Ternary Square-Free Words

Combinatorics 2007-05-23 v1

Authors: Doron Zeilberger

Abstract

We prove that the `connective constant' for ternary square-free words is at least $2^{1/17} = 1.0416 ...$ , improving on Brinkhuis and Brandenburg's lower bounds of $2^{1/24}=1.0293 ...$ and $2^{1/22}=1.032 ...$ respectively. This is the first improvement since 1983.

Keywords

square-free words ternary words connective constant lower bound combinatorics on words

Cite

@article{arxiv.math/9809135,
  title  = {There are More Than 2**(n/17) n-Letter Ternary Square-Free Words},
  author = {Doron Zeilberger},
  journal= {arXiv preprint arXiv:math/9809135},
  year   = {2007}
}

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2 pages (plain TeX)

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