Keränen's infinite word is given as the fixed point of a 85-uniform morphism g85 defined by:
g85(a)=abcacdcbcdcadcdbdabacabadbabcbdbcbacbcdcacbabdabacadcbcdcacdbcbacbcd
cacdcbdcdadbdcbca
g85(b)=σ(h(a))
g85(c)=σ2(h(a))
g85(d)=σ3(h(a))
where σ is a cyclic permutation of letters:
σ: a ↦ b, b ↦ c, c ↦ d, d ↦ a
In
another similar morphism g98 generating abelian-square-free word is given by:
g98(a)=abcacdcbcdcadbdcbdbabcbdcacbabdbabcabdadcdadbdcbd
babdbcbacbcdbabdcdbdcacdbcbacbcdcacdcbdcdadbdcbca
More such morphisms are given in
All the morphisms can be seen and downloaded at
http://south.rotol.ramk.fi/keranen/words2007/a2f.html
It is also known that the number c(n) of abelian-square-free words of length n grows exponentially:
-- StepanHolub - 10 Mar 2012