Counting the number of $\tau$-exceptional sequences over Nakayama algebras

Abstract

The notion of a $\tau$-exceptional sequence was introduced by Buan and Marsh in 2018 as a generalisation of an exceptional sequence for finite dimensional algebras. We calculate the number of complete $\tau$-exceptional sequences over certain classes of Nakayama algebras. In some cases, we obtain closed formulas which also count other well known combinatorial objects and exceptional sequences of path algebras of Dynkin quivers.