On Subword Complexity of Morphic Sequences

TL;DR

This paper investigates the subword complexity of morphic sequences, revealing that their complexity either follows a polynomial pattern of degree related to an integer or grows logarithmically, providing a comprehensive classification.

Contribution

It establishes a clear dichotomy for the subword complexity of morphic sequences, characterizing their growth rates precisely.

Findings

Subword complexity of morphic sequences is either Θ(n^{1+1/k}) or O(n log n).

The paper provides a complete classification of complexity growth rates.

Results apply to pure morphic and morphic sequences.

Abstract

We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n \log n)$.