2014/12/10 by Garver, Alexander, Matherne, Jacob P.
#05E10 (Secondary) #13F60 #16G20 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1412.3365
Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya's work) to classify exceptional sequences of representations of Q, the linearly-ordered quiver with n vertices. We also show how to use variations of this model to classify c-matrices of Q, to interpret exceptional sequences as linear extensions, and to give a simple bijection between exceptional sequences and certain chains in the lattice of noncrossing partitions. In the case of c-matrices, we also give an interpretation of c-matrix mutation in terms of our noncrossing trees with directed edges.