Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.7

The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially

Ali Aberkane & James D. Currie
Department of Mathematics and Statistics
University of Winnipeg
Winnipeg, Manitoba R3B 2E9
Canada

Narad Rampersad
School of Computer Science
University of Waterloo
Waterloo, Ontario N2L 3G1
Canada

Abstract: We show that the number of ternary words of length n avoiding abelian cubes grows faster than r^n, where r = 2^(1/24).

(Concerned with sequence A096168 .)

Received April 7 2004; revised version received June 16 2004. Published in Journal of Integer Sequences June 19 2004.