Errata for ‘The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially

Ali Aberkane, James D. Currie & Narad Rampersad

June 25, 2009

There are a couple of typos:

1. On p. 3, l. 14, read ‘v ∈ h(i − 1)’ for ‘v ∈ h(i)’.

2. On p. 3, l. 15, delete ‘and Σ = Σ′.

On p. 5, l. 13, one must change ‘|3|X_{1}| + 2’ to ‘|3|X_{1}| + 6’. This error propagates:

1. In Lemma 3.3, change ‘|u_{1}| > 17’ to ‘|u_{1}| > 20’. Change all other occurrences of 17 to 21 (on p. 5, l. 10, p. 6, l. 19 & 22.) Change all occurrences of 16 to 20 (on p. 6, l. 23, p. 7, l. 4, 9, 14, 15 & 16.)

2. On p. 7, l. 5 & 6, change all occurrences of a_{1}a_{2}a_{3}a_{4} to a_{1}a_{2}a_{3}a_{4}a_{5} and change ‘a_{1}, a_{2}, a_{3}, a_{4} letters’ to ‘a_{1}, a_{2}, a_{3}, a_{4}, a_{5} letters’. On p. 7, Change ‘length 4’, ‘length4’, ‘Set4’ to ‘length 5’, ‘length5’, ‘Set5’ wherever they occur. In item 2 change 27 to 37; in item 3 change 80 to 146; in item 4 change 278 to 432.

3. In the second last sentence of Section 4, the total time should be given as about 120 seconds.

The results remain valid, and the online code has been modified to correspond to these adjustments.