FREYDENBERGER, D.D., REIDENBACH, D. and SCHNEIDER, J.C., 2005. Unambiguous morphic images of strings. Lecture Notes in Computer Science, 3572, pp. 248-259.
Motivated by the research on pattern languages, we study a fundamental combinatorial question on morphisms in free semigroups: With regard to any string α over some alphabet we ask for the existence
of a morphism σ such that σ(α) is unambiguous, i.e. there is no morphism ρ with ρ ≠ σ and ρ(α) = σ(α). Our main result shows that a rich and natural class of strings is provided with unambiguous morphic images.