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Unambiguous injective morphisms in free groups

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posted on 2022-12-13, 09:22 authored by Joel DayJoel Day, Daniel Reidenbach
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 Computation

Volume

289

Issue

Part A

Publisher

Elsevier

Version

  • VoR (Version of Record)

Rights holder

© The Authors

Publisher 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

2022-07-20

Publication date

2022-07-22

Copyright date

2022

ISSN

0890-5401

eISSN

1090-2651

Language

  • en

Depositor

Dr Joel Day. Deposit date: 29 September 2022

Article number

104946

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