Cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type $A_{ \infty }$

TL;DR

This paper provides a combinatorial classification of cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type A-infinity, advancing understanding of their structure.

Contribution

It introduces a combinatorial framework for classifying cluster tilting subcategories and torsion pairs in these categories, which was not previously established.

Findings

Classification of cluster tilting subcategories

Classification of torsion pairs

New combinatorial methods for infinite type categories

Abstract

We give a combinatorial classification of cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type $A_{ \infty }$.