# The sorting order on a Coxeter group

@article{Armstrong2009TheSO, title={The sorting order on a Coxeter group}, author={Drew Armstrong}, journal={J. Comb. Theory, Ser. A}, year={2009}, volume={116}, pages={1285-1305} }

Let (W,S) be an arbitrary Coxeter system. For each word @w in the generators we define a partial order-called the @w-sorting order-on the set of group elements W"@w@?W that occur as subwords of @w. We show that the @w-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and Bruhat orders on the group. Moreover, the @w-sorting order is a ''maximal lattice'' in the sense that the addition of any collection of Bruhat covers results in a nonlattice… Expand

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