Unambiguous 1-uniform morphisms

Morphic Primitivity and Alphabet Reductions

“…Our main result in this section strengthens our results in [7] regarding the existence of unambiguous alphabet reductions φ : N * → ∆ * , ∆ ⊂ N, for a fixed target alphabet (i. e., the size of ∆ does not depend on the number of letters in the preimage). The overall goal of most of the papers on unambiguous morphisms is to characterise the set of words that have an unambiguous morphism, and this goal has so far been accomplished for general nonerasing morphisms in two different settings (see Section 1).…”

“…In [7] we have provided some results indicating that an equivalent phenomenon might hold with regard to Problem 1. Our first main result in the present paper shows that this indeed is true.…”

“…In contrast to this, for variable target alphabets (i. e., the size of the target alphabet depends on the number of letters in the given word), [7] conjectures that the problem has a nice and compact solution:…”

“…The research on the ambiguity of morphisms was initiated by Freydenberger, Reidenbach and Schneider [3], and previous papers on this subject mainly focus on the question of whether unambiguous morphisms exist for a given word (see Schneider [10], Reidenbach and Schneider [9], Freydenberger, Nevisi and Reidenbach [2] and Nevisi and Reidenbach [7]). In [7] we have investigated this problem for 1-uniform morphisms, providing some first insights into it.…”

“…In [7] we have investigated this problem for 1-uniform morphisms, providing some first insights into it. In the first technical part of present paper we wish to continue this research, thus studying the following question: Problem 1.…”