On a conjecture about finite fixed points of morphisms
A conjecture of M. Billaud is: given a word w, if, for each letter x occurring in w, the word obtained by erasing all the occurrences of x in w is a fixed point of a nontrivial morphism f(x) then w is also a fixed point of a non-trivial morphism. We prove that this conjecture is equivalent to a similar one on sets of words. Using this equivalence, we solve these conjectures in the particular case where each morphism f(x) has only one expansive letter. (c) 2005 Elsevier B.V. All rights reserved.
fixed points morphisms combinatorics on words