On abelian and additive complexity in infinite words
Hayri Ardal, Tom Brown, Veselin Jungi\'c, Julian Sahasrabudhe
TL;DR
This paper explores the structure of infinite words with bounded abelian and additive complexities, introducing bounded additive complexity and providing an alternative proof of existing results.
Contribution
It defines bounded additive complexity for infinite words over Z^m and offers a new proof of a key result in the field.
Findings
Introduction of bounded additive complexity concept
Alternative proof of a known result on abelian complexity
Enhanced understanding of infinite word structures
Abstract
The study of the structure of infinite words having bounded abelian complexity was initiated by G. Richomme, K. Saari, and L. Q. Zamboni. In this note we define bounded additive complexity for infinite words over a finite subset of Z^m. We provide an alternative proof of one of the results of Richomme, Saari, and Zamboni.
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Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · Computability, Logic, AI Algorithms