The classification of \tau-tilting modules over Nakayama algebras

TL;DR

This paper explores tau-tilting modules over Nakayama algebras, establishing bijections with polygon triangulations and integer sequences, and provides an algorithm for constructing the support tau-tilting modules' Hasse quiver.

Contribution

It introduces new bijections connecting tau-tilting modules with geometric and combinatorial objects, and offers an algorithm for visualizing their structure.

Findings

Bijections between tau-tilting modules and polygon triangulations

Bijections between tau-tilting modules and integer sequences

Algorithm for constructing the Hasse quiver of support tau-tilting modules

Abstract

In this paper, we study tau-tilting modules over Nakayama algebras. We establish bijections between tau-tilting modules, triangulations of a polygon with a puncture and certain integer sequences. Moreover, we give an algorithm to construct the Hasse quiver of support tau-tilting modules by using Rejection Lemma of Drozd-Kirichenko.