Paper on Integer Sequences

I recently published a paper in the Journal of Integer Sequences titled An Improved Lower Bound on the Number of Ternary Squarefree Words.

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: \( 952^{n/53} \approx 1.1381531^n \).

Paper and Supplementary Material

Citation
 
M. Sollami, C. Douglas, M. Liebmann. An Improved Lower Bound on the Number of Ternary Squarefree Words. Journal of Integer Sequences. Vol. 19 (2016), Article 16.6.7