An Improved Lower Bound for $n$Brinkhuis $k$Triples
Abstract
Let $s_n$ be the number of words consisting of the ternary alphabet consisting of the digits 0, 1, and 2 such that no subword (or factor) is a square (a word concatenated with itself, e.g., $11$, $1212$, or $102102$). From computational evidence, $s_n$ grows exponentially at a rate of about $1.317277^n$. While known upper bounds are already relatively close to the conjectured rate, effective lower bounds are much more difficult to obtain. In this paper, we construct a $54$Brinkhuis $952$triple, which leads to an improved lower bound on the number of $n$letter ternary squarefree words: $952^{n/53} \approx 1.1381531^n$.
 Publication:

arXiv eprints
 Pub Date:
 June 2016
 DOI:
 10.48550/arXiv.1606.00835
 arXiv:
 arXiv:1606.00835
 Bibcode:
 2016arXiv160600835S
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Formal Languages and Automata Theory
 EPrint:
 21 pages