Abelian antipowers in infinite words
An abelian antipower of order k (or simply an abelian k-antipower) is a concatenation of k consecutive words of the same length having pairwise distinct Parikh vectors. This definition generalizes to the abelian setting the notion of a k-antipower, as introduced in Fici et al. (2018) [7], that is a...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://doi.org/10.1016/j.aam.2019.04.001 |
| Country: | Portugal |
| Oai: | oai:run.unl.pt:10362/75564 |
| Summary: | An abelian antipower of order k (or simply an abelian k-antipower) is a concatenation of k consecutive words of the same length having pairwise distinct Parikh vectors. This definition generalizes to the abelian setting the notion of a k-antipower, as introduced in Fici et al. (2018) [7], that is a concatenation of k pairwise distinct words of the same length. We aim to study whether a word contains abelian k-antipowers for arbitrarily large k. Š. Holub proved that all paperfolding words contain abelian powers of every order (Holub, 2013 [8]). We show that they also contain abelian antipowers of every order. |
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