Similarly, there is an affine analogue of descents in permutations: an affine permutation u has a descent in position i if u ( i ) > u ( i + 1 ) . (By periodicity, u has a descent in position i if and only if it has a descent in position i + k n for all integers k.) Algebraically, the descents corresponds to the right descents in the sense of Coxeter groups; that is, i is a descent of u if and only if ℓ ℓ ( u ⋅ ⋅ s i ) < ℓ ℓ ( u ) . The left descents (that is, those indices i such that ℓ ℓ ( s i ⋅ ⋅ u ) < ℓ ℓ ( u ) ) are the descents of the inverse affine permutation u − − 1 ; equivalently, they are the values i such that i occurs before i − 1 in the sequence … … , u ( − − 2 ) , u ( − − 1 ) , u ( 0 ) , u ( 1 ) , u ( 2 ) , … … . Geometrically, i is a descent of u if and only if the fixed hyperplane of s i separates the alcoves A 0 and A 0 ⋅ ⋅ u .