The authors define second higher Bruhat orders as posets on commutation classes of reduced words for any affine permutation and prove direct analogs of classical results for all higher orders in the symmetric group.
Extension spaces of oriented matroids
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Commutation classes of reduced words and higher Bruhat orders for affine permutations
The authors define second higher Bruhat orders as posets on commutation classes of reduced words for any affine permutation and prove direct analogs of classical results for all higher orders in the symmetric group.