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

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

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).

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(Concerned with sequence A096168 .)

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

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