A Rauzy fractal unbounded in all directions of the plane

2021/02/04 by Andrieu, Mélodie · 2 citations
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.02497

Abstract

We construct an Arnoux-Rauzy word for which the set of all differences of two abelianized factors is equal to ℤ³. In particular, the imbalance of this word is infinite - and its Rauzy fractal is unbounded in all directions of the plane.

Cited by

• A proof of Rauzy's conjecture on abelian complexity
• New examples of words for which binomial complexities and subword complexity coincide

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