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Download fileUnambiguous injective morphisms in free groups
A morphism g is ambiguous with respect to a word u if there exists a second morphism h≠g such that g(u)=h(u). Otherwise g is unambiguous with respect to u. Thus unambiguous morphisms are those for which the structure of the morphism is preserved in the image. Ambiguity has so far been studied for morphisms of free monoids, where several characterisations exist for the set of words u permitting an (injective) unambiguous morphism. In the present paper, we consider ambiguity of morphisms of free groups, and consider possible analogies to the existing characterisations in the free monoid. While a direct generalisation results in a trivial situation where all morphisms are ambiguous, we discuss some natural and well-motivated reformulations, and provide a characterisation of words in a free group that permit a morphism which is “as unambiguous as possible”.
History
School
- Science
Department
- Computer Science
Published in
Information and ComputationVolume
289Issue
Part APublisher
ElsevierVersion
- VoR (Version of Record)
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© The AuthorsPublisher statement
This is an Open Access Article. It is published by Elsevier under the Creative Commons Attribution 4.0 International Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/Acceptance date
2022-07-20Publication date
2022-07-22Copyright date
2022ISSN
0890-5401eISSN
1090-2651Publisher version
Language
- en