Given a tree embedded in a disk, we define two lattices-the oriented flip graph of
noncrossing arcs and the lattice of noncrossing tree partitions. When the interior vertices of …

The purpose of this paper is to understand lattices of certain subcategories in module
categories of representation-finite gentle algebras called tiling algebras, as introduced by …

We introduce weak exceptional sequence of modules which can be viewed as another
modification of the standard case, different from the works of Igusa-Todorov [IT17] and Buan …

We prove that there is a one-to-one correspondence between the following three sets:
idempotent functions on a set of size n, complete exceptional sequences of linear radical …

The notion of a τ-exceptional sequence was introduced by Buan and Marsh in as a
generalisation of an exceptional sequence for finite dimensional algebras. We calculate the …

This thesis is concerned with various aspects of the representation the-ory of finite
dimensional algebras, with a focus on combinatorial and homological aspects. We explore …