WORDS 2017: Combinatorics on Words pp 72-84

# Equations Enforcing Repetitions Under Permutations

• Joel D. Day
• Pamela Fleischmann
• Florin Manea
• Dirk Nowotka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10432)

## Abstract

The notion of repetition of factors in words is central to combinatorics on words. A recent generalisation of this concept considers repetitions under permutations: give an alphabet $$\Sigma$$ and a morphism or antimorphism f on $$\Sigma ^*$$, whose restriction to $$\Sigma$$ is a permutation, w is an [f]-repetition if there exists $$\gamma \in \Sigma ^*$$ such that $$w=f^{i_1}(\gamma )f^{i_2}(\gamma )\cdots f^{i_k}(\gamma )$$, for some $$k\ge 2$$. 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.

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© Springer International Publishing AG 2017

## Authors and Affiliations

• Joel D. Day
• 1
• Pamela Fleischmann
• 1
• Florin Manea
• 1
• Dirk Nowotka
• 1
1. 1.Institut für InformatikChristian-Albrechts-Universität zu KielKielGermany