The notion of a τ-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 τ-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.

中文翻译：

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计算 Nakayama 代数上 τ-异常序列的数量

Buan 和 Marsh 在 (2018) 中引入了τ -异常序列的概念，作为有限维代数异常序列的推广。我们计算某些类别的 Nakayama 代数上的完整τ -异常序列的数量。在某些情况下，我们获得了封闭公式，这些公式也计算了其他众所周知的组合对象，以及 Dynkin quivers 的路径代数的特殊序列。