Minimal Complexities for Infinite Words Written with d Letters

Andrieu, Mélodie; Vivion, Léo

doi:10.1007/978-3-031-33180-0_1

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2024

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“…Another well-known generalization is represented by hypercubic billiard sequences generated by momenta with rationally independent components. Ternary hypercubic billiard sequences are 2-balanced [6] and under some additional condition on momentum, their factor complexity equals n 2 + n + 1 (see [7][8][9]). The class contains sequences of any given rationally independent frequencies.…”

Section: Introductionmentioning

confidence: 99%

2-balanced sequences coding rectangle exchange transformation

Dvořáková,

Masáková,

Pelantová

2024

Preprint

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We define a new class of ternary sequences that are 2-balanced. These sequencesare obtained by colouring of Sturmian sequences. We show that the class containssequences of any given letter frequencies. We provide an upper bound on factorand abelian complexity of these sequences. Using the interpretation by rectangleexchange transformation, we prove that for almost all triples of letter frequencies,the upper bound on factor and abelian complexity is reached. The bound onfactor complexity is given using a number-theoretical function which we computeexplicitly for a class of parameters. MSC Classification: 68R15

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