Publicação
Abelian antipowers in infinite words
| Resumo: | 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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| Autores principais: | Fici, Gabriele |
| Outros Autores: | Postic, Mickael; Silva, Manuel |
| Assunto: | Abelian antipower Abelian complexity k-antipower Paperfolding word Sierpiǹski word Applied Mathematics |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | 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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