Exceptional Sequences and Idempotent Functions

Abstract

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 $\sum _{j=1}^n\left(\genfrac{}{}{0ex}{}{n}{j}\right)j^{n-j}$.

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• Weak Exceptional Sequences