A Uniqueness Property of \(\tau \)-Exceptional Sequences

Abstract

Recently, Buan and Marsh showed that if two complete \(\tau \)-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is \(\tau \)-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 \(\tau \)-exceptional sequence are linearly independent.