Abelian antipowers in infinite words

Gabriele Fici, Mickael Postic, Manuel Silva

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Abstract

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.

Original languageEnglish
Pages (from-to)67-78
Number of pages12
JournalAdvances in Applied Mathematics
Volume108
DOIs
Publication statusPublished - 1 Jul 2019

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Infinite Words
Concatenation
Pairwise
Distinct
Consecutive
Generalise

Keywords

  • Abelian antipower
  • Abelian complexity
  • k-antipower
  • Paperfolding word
  • Sierpiǹski word

Cite this

Fici, Gabriele ; Postic, Mickael ; Silva, Manuel. / Abelian antipowers in infinite words. In: Advances in Applied Mathematics. 2019 ; Vol. 108. pp. 67-78.
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Abelian antipowers in infinite words. / Fici, Gabriele; Postic, Mickael; Silva, Manuel.

In: Advances in Applied Mathematics, Vol. 108, 01.07.2019, p. 67-78.

Research output: Contribution to journalArticle

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