BALANCE PROPERTIES OF ARNOUX–RAUZY WORDS

DOI10.1142/S0218196713400043zbMath1269.68073arXiv1212.5106MaRDI QIDQ2842015

Wolfgang Steiner, Julien Cassaigne, Valérie Berthé

Publication date: 30 July 2013

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.5106

zbMATH Keywords

infinite wordsArnoux-Rauzy words\(S\)-adic sequencesbalance properties

Mathematics Subject Classification ID

Combinatorics on words (68R15) Symbolic dynamics (37B10)

Related Items (8)

Geometry, dynamics, and arithmetic of $S$-adic shifts ⋮ Balancedness and coboundaries in symbolic systems ⋮ Critical Exponents of Regular Arnoux-Rauzy Sequences ⋮ On a Class of 2-Balanced Sequences ⋮ On non-repetitive complexity of Arnoux-Rauzy words ⋮ An upper bound on asymptotic repetition threshold of balanced sequences via colouring of the Fibonacci sequence ⋮ S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry ⋮ Abelian properties of Parry words

Cites Work

• On the superimposition of Christoffel words
• Substitutions in dynamics, arithmetics and combinatorics
• On a generalization of Christoffel words: epichristoffel words
• Weak mixing and eigenvalues for Arnoux-Rauzy sequences
• Balance and abelian complexity of the Tribonacci word
• Sturmian morphisms, the braid group \(B_4\), Christoffel words and bases of \(F_2\)
• Fine and Wilf's theorem for three periods and a generalization of Sturmian words
• Imbalances in Arnoux-Rauzy sequences
• Well-balanced sequences
• Bifix codes and Sturmian words
• Recurrence functions of Arnoux-Rauzy sequences, and answer to a question of Morse and Hedlund
• On an involution of Christoffel words and Sturmian morphisms
• On Christoffel classes
• Combinatorics on Words
• Représentation géométrique de suites de complexité $2n+1$
• Episturmian words: a survey

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