τ-exceptional sequences

We introduce the notions of τ-exceptional and signed τ-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank n, and for any positive integer t ≤ n, there is a bijection between the set of signed τ-exceptional sequences of length, and (basic) ordered support τ-rigid objects within decomposable direct summands. If the algebra is hereditary, our notions coincide with exceptional and signed exceptional sequences. The latter were recently introduced by Igusa and Todorov, who constructed a similar bijection in the hereditary setting