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The Shard Intersection Order on Permutations

By Erin Bancroft

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

Topics: Mathematics - Combinatorics, 05A05 (Primary), 20F55, 52C35, 06B10 (Secondary)
Year: 2011
OAI identifier: oai:arXiv.org:1103.1910
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