A generalization of perfectly clustering words and band bricks for certain gentle algebras

TL;DR

This paper extends the concept of perfectly clustering words to a broader class of gentle algebras, establishing new connections and proving a generalized conjecture in the field.

Contribution

It generalizes the notion of perfectly clustering words and relates them to band bricks over certain gentle algebras, proving a broader conjecture.

Findings

Generalization of perfectly clustering words.

Relation between clustering words and band bricks.

Proof of a generalized conjecture.

Abstract

We generalize the perfectly clustering words of Simpson and Puglisi and relate them to band bricks over certain gentle algebras. This allows us to prove a generalization of a conjecture by the second author on perfectly clustering words.