A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments (h,g,1). In particular, when h=Θ(n7/15) and g=Θ(h1/5), the average running time is O(n23/15). The proof involves interesting properties of the inversions in random permutations that have been h-sorted and g-sorted.
Cite
@article{arxiv.cs/9608105,
title = {Shellsort with three increments},
author = {Svante Janson and Donald E. Knuth},
journal= {arXiv preprint arXiv:cs/9608105},
year = {2008}
}