2-balanced sequences coding rectangle exchange transformation

Lubomíra Dvořáková, Zuzana Masáková, Edita Pelantová

Published 2024-03-19Version 1

We define a new class of ternary sequences that are 2-balanced. These sequences are obtained by colouring of Sturmian sequences. We show that the class contains sequences of any given letter frequencies. We provide an upper bound on factor and abelian complexity of these sequences. Using the interpretation by rectangle exchange transformation, we prove that for almost all triples of letter frequencies, the upper bound on factor and abelian complexity is reached. The bound on factor complexity is given using a number-theoretical function which we compute explicitly for a class of parameters.