Abelian antipowers in infinite words

Gabriele Fici; Mickael Postic; Manuel Silva

doi:10.1016/j.aam.2019.04.001

Abelian antipowers in infinite words

Gabriele Fici, Mickael Postic, Manuel Silva

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	67-78
Number of pages	12
Journal	Advances in Applied Mathematics
Volume	108
DOIs	https://doi.org/10.1016/j.aam.2019.04.001
Publication status	Published - 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, G., Postic, M., & Silva, M. (2019). Abelian antipowers in infinite words. Advances in Applied Mathematics, 108, 67-78. https://doi.org/10.1016/j.aam.2019.04.001

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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Fici, G, Postic, M & Silva, M 2019, 'Abelian antipowers in infinite words' Advances in Applied Mathematics, vol. 108, pp. 67-78. https://doi.org/10.1016/j.aam.2019.04.001

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 journal › Article

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