Permutation complexity of images of Sturmian words by marked morphisms

TL;DR

This paper proves that applying a binary marked morphism to a Sturmian word results in an image whose permutation complexity grows linearly with the length, specifically as n plus a constant, for large n.

Contribution

It establishes a precise linear growth pattern for permutation complexity of Sturmian words under binary marked morphisms, extending understanding of their combinatorial structure.

Findings

Permutation complexity of the image is n + k for large n.

Growth pattern is linear with a constant offset.

Results apply to all sufficiently large word lengths.

Abstract

We show that the permutation complexity of the image of a Sturmian word by a binary marked morphism is $n+k$ for some constant $k$ and all lengths $n$ sufficiently large.