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 |
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Pages (from-to) | 67-78 |
Number of pages | 12 |
Journal | Advances in Applied Mathematics |
Volume | 108 |
DOIs | |
Publication status | Published - 1 Jul 2019 |
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Keywords
- Abelian antipower
- Abelian complexity
- k-antipower
- Paperfolding word
- Sierpiǹski word
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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 journal › Article
TY - JOUR
T1 - Abelian antipowers in infinite words
AU - Fici, Gabriele
AU - Postic, Mickael
AU - Silva, Manuel
PY - 2019/7/1
Y1 - 2019/7/1
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.
KW - Abelian antipower
KW - Abelian complexity
KW - k-antipower
KW - Paperfolding word
KW - Sierpiǹski word
UR - http://www.scopus.com/inward/record.url?scp=85063954465&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2019.04.001
DO - 10.1016/j.aam.2019.04.001
M3 - Article
VL - 108
SP - 67
EP - 78
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
SN - 0196-8858
ER -