### Abstract

Original language | English |
---|---|

Pages (from-to) | 67-78 |

Number of pages | 12 |

Journal | Advances in Applied Mathematics |

Volume | 108 |

Publication status | Published - 2019 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

*Advances in Applied Mathematics*,

*108*, 67-78.

**Abelian antipowers in infinite words.** / Fici, Gabriele; Silva, Manuel; Postic, Mickael.

Research output: Contribution to journal › Article

*Advances in Applied Mathematics*, vol. 108, pp. 67-78.

}

TY - JOUR

T1 - Abelian antipowers in infinite words

AU - Fici, Gabriele

AU - Silva, Manuel

AU - Postic, Mickael

PY - 2019

Y1 - 2019

N2 - 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

AB - 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

UR - http://hdl.handle.net/10447/372617

UR - http://www.elsevier.com/inca/publications/store/6/2/2/7/7/6/index.htt

M3 - Article

VL - 108

SP - 67

EP - 78

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

ER -