2-balanced sequences coding rectangle exchange transformation
Combinatorics
2024-03-20 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2403.12791,
title = {2-balanced sequences coding rectangle exchange transformation},
author = {Lubomíra Dvořáková and Zuzana Masáková and Edita Pelantová},
journal= {arXiv preprint arXiv:2403.12791},
year = {2024}
}