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.
D. Nowotka—Research supported by DFG grant NO 872/3-2 (jda, dn), DFG grant MA 5725/1-2 (flm), BMBF HPSV grant 01IH15006A (fpa).
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Day, J.D., Fleischmann, P., Manea, F., Nowotka, D. (2017). Equations Enforcing Repetitions Under Permutations. In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham. https://doi.org/10.1007/978-3-319-66396-8_8
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