A Taxonomy of Morphic Sequences

TL;DR

This paper provides a comprehensive classification of sequences based on morphic properties, establishing the existence or non-existence of examples for each category.

Contribution

It introduces a detailed taxonomy of morphic sequences, clarifying the relationships and boundaries among various subclasses.

Findings

Classifies sequences into morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, and pure primitive morphic.

Provides examples or proves non-existence for each category.

Enhances understanding of the structure and diversity of morphic sequences.

Abstract

In this note we classify sequences according to whether they are morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, or pure primitive morphic, and for each possibility we either give an example or prove that no example is possible.