The reflection length ℓ ℓ R ( u ) of an element u of S ~ ~ n is the smallest number k such that there exist reflections r 1 , … … , r k such that u = r 1 ⋯ ⋯ r k . (In the symmetric group, reflections are transpositions, and the reflection length of a permutation u is n − − c ( u ) , where c ( u ) is the number of cycles of u.) In (Lewis et al. 2019), the following formula was proved for the reflection length of an affine permutation u : for each cycle of u, define the weight to be the integer k such that consecutive entries congruent modulo n differ by exactly kn. Form a tuple of cycle weights of u (counting translates of the same cycle by multiples of n only once), and define the nullity ν ν ( u ) to be the size of the smallest set partition of this tuple so that each part sums to 0. Then the reflection length of u is ℓ ℓ R ( u ) = n − − 2 ν ν ( u ) + c ( π π ( u ) ) , where π π ( u ) is the underlying permutation of u.