The Shard Intersection Order on Permutations

Details The Shard Intersection Order on Permutations The Shard Intersection Order on Permutations

2011-03-09

arxiv.org/abs/1103.1910v1

Mathematics

Combinatorics

This is part of my dissertation at North Carolina State University supervised by Dr. Nathan Reading. 19 pages, 9 figures

Scientific paper

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.

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