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Equations enforcing repetitions under permutations

journal contribution
posted on 16.10.2020 by Joel Day, Pamela Fleischmann, Florin Manea, Dirk Nowotka
© 2020 Elsevier B.V. The notion of repetition of factors in words is central to combinatorics on words. A recent generalisation of this concept considers repetitions under permutations: given an alphabet Σ and a morphism or antimorphism f on Σ∗, whose restriction to Σ is a permutation, w is an [f]-repetition if there exists γ∈Σ∗, an integer k≥2, and the positive integers i1,…,ik such that w=fi1(γ)fi2(γ)⋯fik(γ). In this paper, we extend a series of classical repetition enforcing word equations to this general setting to obtain a series of word equations whose solutions are [f]-repetitions.

Funding

Deutsche Forschungsgemeinschaft (DFG), Germany grant 389613931.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Discrete Applied Mathematics

Volume

285

Pages

61 - 78

Publisher

ELSEVIER

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Discrete Applied Mathematics and the definitive published version is available at https://doi.org/10.1016/j.dam.2020.05.026

Acceptance date

23/05/2020

Publication date

2020-06-15

Copyright date

2020

ISSN

0166-218X

eISSN

1872-6771

Language

en

Depositor

Dr Joel Day Deposit date: 14 October 2020

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