Combinatorics of exceptional sequences in type A
Abstract
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 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.
Cite
@article{arxiv.1506.08927,
title = {Combinatorics of exceptional sequences in type A},
author = {Alexander Garver and Kiyoshi Igusa and Jacob P. Matherne and Jonah Ostroff},
journal= {arXiv preprint arXiv:1506.08927},
year = {2016}
}
Comments
21 pages. Made changes throughout to improve the exposition, and made changes suggested by an anonymous referee. arXiv admin note: text overlap with arXiv:1412.3365