A uniqueness property of τ exceptional sequences

Abstract

Recently, Buan and Marsh showed that if two complete $\ddot{I}„$-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is $\ddot{I}„$-tilting finite. They conjectured that the result holds without that assumption. We prove their conjecture. Along the way, we also show that the dimension vectors of the modules in a $\ddot{I}„$-exceptional sequence are linearly independent.

v2: journal accepted manuscript. 7 pages