  We prove a lower bound expressed in the increment sequence on the
average-case complexity of the number of inversions of Shellsort. This lower
bound is sharp in every case where it could be checked. A special case of this
lower bound yields the general Jiang-Li-Vit\'anyi lower bound. We obtain new
results e.g. determining the average-case complexity precisely in the
Yao-Janson-Knuth 3-pass case.
