Counting the number of $τ$-exceptional sequences over Nakayama algebras

关于一类Nakayama代数上例外对的数量

On the Number of Exceptional Pairs Over a Class of Nakayama Algebras

本文利用组合与同调方法，为若干Nakayama代数及根平方零代数的Auslander代数推导出例外对数量的显式公式，并揭示其与OEIS整数序列的联系。

具有τ-例外序列的braiding群作用的Nakayama代数分类

Classifying Nakayama algebras with a braid group action on $τ$-exceptional sequences

本文研究了具有τ-例外序列的braiding群作用的Nakayama代数，证明其突变保持braiding群关系的条件是代数为hereditary或不可分解项目性模的长度满足特定要求。

有序 $τ$-刚性模的突变及其在 Nakayama 代数中的应用

Mutating ordered $τ$-rigid modules with applications to Nakayama algebras

本文通过 TF-有序 $τ$-刚性模解释 $τ$-例外序列的突变，并利用显式组合描述证明 Nakayama 代数上突变的传递性。

Braid action on derived category of Nakayama algebras

We construct an action of a braid group associated to a complete graph on the derived category of a certain symmetric Nakayama algebra which is also a Brauer star algebra with no exceptional vertex. We connect this action with the affine braid group action on Brauer star algebras defined by Schaps and Zakay-Illouz. We show that for Brauer star algebras with no exceptional vertex, the action is faithful.

Exceptional Sequences and Idempotent Functions

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 square zero Nakayama algebras of rank $n$ and rooted labeled forests with $n$ nodes and height of at most one. Therefore, the number of exceptional sequences is given by the sum $\sum\limits^n_{j=1}\binom{n}{j}j^{n-j}$.

Weak Exceptional Sequences

We introduce weak exceptional sequence of modules which can be viewed as another modification of the standard case, different than the works of Igusa-Todorov \cite{Igusa-Todorov} and Buan-Marsh \cite{Buan-Marsh}. For hereditary algebras it is equivalent to standard exceptional sequences. One important new feature is: if global dimension of algebra is greater than one, then the size of the full sequence can exceed the rank of the algebra. We use both cyclic and linear Nakayama algebras to test combinatorial aspects of this new sequence. For some particular classes we give closed form formulas w…