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RESEARCH PRODUCT

Abelian antipowers in infinite words

Manuel SilvaGabriele FiciMickael Postic

subject

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniSierpiǹski wordSettore INF/01 - InformaticaApplied MathematicsConcatenationAbelian complexityCombinatoricsArbitrarily largeOrder (group theory)Pairwise comparisonk-antipowerAbelian groupPaperfolding wordComputer Science::Formal Languages and Automata TheoryWord (group theory)Abelian antipowerMathematics

description

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. S. 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.

yearjournalcountryeditionlanguage
2019-07-01Advances in Applied Mathematics
https://doi.org/10.1016/j.aam.2019.04.001