%0 DATA
%A Hossein, Nevisi
%A Daniel, Reidenbach
%D 2012
%T Morphic primitivity and alphabet reductions
%U https://repository.lboro.ac.uk/articles/Morphic_primitivity_and_alphabet_reductions/9405476
%2 https://repository.lboro.ac.uk/ndownloader/files/17022188
%K Combinatorics on words
%K Morphisms
%K Ambiguity
%K Morphic primitivity
%K Fixed points
%K Billaud's Conjecture
%X An alphabet reduction is a 1-uniform morphism that maps
a word to an image that contains a smaller number of dfferent letters.
In the present paper we investigate the effect of alphabet reductions on
morphically primitive words, i. e., words that are not a fixed point of
a nontrivial morphism. Our first main result answers a question on the
existence of unambiguous alphabet reductions for such words, and our
second main result establishes whether alphabet reductions can be given
that preserve morphic primitivity. In addition to this, we study Billaud's
Conjecture - which features a dfferent type of alphabet reduction, but
is otherwise closely related to the main subject of our paper - and prove
its correctness for a special case.