2011/03/09 by Erin Bancroft, Bancroft, Erin
Mathematics · Engineering · Computer Science · #Advanced Combinatorial Mathematics #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1103.1910
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.