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

TL;DR

This paper establishes a new lower bound for the growth rate of ternary square-free words, showing it exceeds previous bounds for the first time since 1983, indicating a richer combinatorial structure.

Contribution

The paper improves the known lower bound for the connective constant of ternary square-free words from 2^{1/22} to 2^{1/17}, the first such enhancement since 1983.

Findings

Lower bound for connective constant increased to 2^{1/17}

Demonstrates richer structure of ternary square-free words

First improvement in bounds since 1983

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.