An abelian square is a word of the form xx , |x|=|x | > 0, with x a permutation of x. An example in English is reappear. Similarly, an abelian cube is a word of the form xx x, |x|=|x |=|x| > 0, with x and x both permutations of x. An example in English is deeded.

(a) Does there exist an infinite word over a three-letter alphabet avoiding abelian squares xx with |x|=|x | 2?

(b) Does there exist an infinite word over a two-letter alphabet avoiding abelian cubes xx x with |x|=|x |=|x| 2?