Arnoux–Rauzy Substitutions and Palindrome Words

  • Hamdi Ammar
  • Tarek SellamiEmail author


We consider \(\sigma _1, \sigma _2, \sigma _3\) the Arnoux–Rauzy substitutions. In this paper we study Palindrome words on the Arnoux–Rauzy substitutions sequences. We prove that the product \(\sigma _i\sigma _j^{k_2}\sigma _s^{k_3}(i)\) is a Palindrome word, where \(i,j,s\in \{1,2,3 ;i\ne j\ne s\}\) and \(k_2,k_3\in {\mathbb {N}}^*\).


Substitutions Arnoux–Rauzy substitutions S-adic Combinatorics on words Finite words 

Mathematics Subject Classification

28A80 11B85 37B10 


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences of SfaxSfax UniversitySfaxTunisia

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