Abelian Square-Free Partial Words

The following applet generates abelian square-free words. Provide the alphabet size and the desired length and then click the 'Create' button. Note, the number of abelian square-free words grows exponentially. Long lengths will increase generation time considerably. The program generates the abelian square-free words by combining abelian square-free factors of lengths 2 and 1. For example, for a length 9 word, it will combine 4 length-2 factors and one length-1 factor. Also, you can provide an expression in the third field below and the generator will only produce words matching that expression. To represent any letter (a wildcard), use period . and use apostrophe ' for holes. You can specify letters at particular indices by using lowercase letters starting from the beginning of the alphabet. For example, using an alphabet size of 4 and the expression "a.'..b" gives us the abelian square-free words: ad'cab, ab'cdb, ac'dab, ab'dcb. By starting a new job, you halt the old one.

The executable jar file with save capabilities is available here.

The implementation of our results requires Java 1.6 or higher from Sun Microsystems.

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