LAUSR

Abstract Let ( W , S ) be the affine Weyl group of type C ˜ n with S its Coxeter generator set. Let Λ ‾ 2 n + 1 be the set of all partitions λ = ( λ 1 , . . . , λ r ) of 2 n + 1 such that ∑ j = 1 2 k + 1 λ j is odd for any k ∈ N with 2 k + 1 ⩽ r . For any J ⊊ S , let w J be the longest element in the parabolic subgroup of W generated by J. We define a map ϕ ‾ : { w J | J ⊊ S } ⟶ Λ ‾ 2 n + 1 and study the preorder ⩽ LR on the set { w J | J ⊊ S } and its relation with the partial order ⩽ on the set { ϕ ‾ ( w J ) | J ⊊ S } , where iterating star operations and primitive pairs play an important role.