On the Ambiguity of Erasing Morphisms

This book discusses a very basic and fundamental phenomenon in combinatorics on words, namely the ambiguity of morphisms: A morphism h is called ambiguous for a word w provided that there is another morphism g which satisfies g(w)=h(w). If such another morphism does not exist, h is called unambiguous for w. Furthermore, there are different types of restricted ambiguity which make additional demands on the other morphism g. The examination of the ambiguity of morphisms is not only of intrinsic interest, but, due to the simplicity of the concept, also shows various connections to other topics in theoretical computer science and discrete mathematics, pattern languages and various other concepts as fixed points of morphisms, avoidable patterns and word equations. This book is the first comprehensive study of the ambiguity of erasing morphisms, i., e., morphisms that are allowed to map symbols in the word to the empty word