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arXiv · 1103.1910

The Shard Intersection Order on Permutations

Erin Bancroft
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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.

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Erin Bancroft. 2011-03-09. The Shard Intersection Order on Permutations. https://arxiv.org/abs/1103.1910

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