  Exceptional sequences are certain ordered sequences of quiver
representations. We introduce a class of objects called strand diagrams and use
this model to classify exceptional sequences of representations of a quiver
whose underlying graph is a type $A_n$ Dynkin diagram. We also use variations
of this model to classify c-matrices of such quivers, to interpret exceptional
sequences as linear extensions of posets, and to give a simple bijection
between exceptional sequences and certain chains in the lattice of noncrossing
partitions. This work extends a classification of exceptional sequences for the
linearly-ordered quiver obtained in an earlier paper by the first and third
authors.
