The Shard Intersection Order on Permutations
Combinatorics
2011-03-11 v1
Abstract
The shard intersection order is a new lattice structure on a finite Coxeter group W which encodes the geometry of the reflection arrangement and the lattice theory of the weak order. In the case where W is the symmetric group, we characterize shard intersections as certain pre-orders which we call permutation pre-orders. We use this combinatorial characterization to determine properties of the shard intersection order. In particular, we give an EL-labeling.
Cite
@article{arxiv.1103.1910,
title = {The Shard Intersection Order on Permutations},
author = {Erin Bancroft},
journal= {arXiv preprint arXiv:1103.1910},
year = {2011}
}
Comments
This is part of my dissertation at North Carolina State University supervised by Dr. Nathan Reading. 19 pages, 9 figures