Exceptional Sequences over path algebras of type $A_n$ and Non-crossing Spanning Trees

TL;DR

This paper classifies all complete exceptional sequences over path algebras of type A_n quivers using non-crossing spanning trees, linking algebraic structures with combinatorial models.

Contribution

It provides a complete classification of exceptional sequences for type A_n algebras via a combinatorial approach involving non-crossing spanning trees.

Findings

Complete classification of exceptional sequences for type A_n

Connection established between algebraic and combinatorial structures

Framework for understanding derived categories of type A_n algebras

Abstract

Exceptional sequences are fundamental to investigate the derived categories of finite dimensional algebras. The aim of this note is to classify all the complete exceptional sequences over the path algebra of a Dynkin quiver of type $A_n$ in terms of non-crossing spanning trees.