While studying the standard method for random permutation generation I discovered a function whose distribution on a uniformly random permutation of fixed length is the same as that of the number of inversions. Such things are called Mahonian permutation statistics.
This statistic appears to be new, but this is not as easy to show as I would like. After several attempts to find out by reading papers, asking experts and doing database searches, I concluded that it probably was and submitted the paper to the arXiv and for publication. Almost immediately I got email from Dennis White at University of Minnesota pointing out a connection with a paper by him and Galovich in 1996. This raises some questions: how much responsibility do we have in the modern research environment to check novelty? why is there no standard database of numerical values of all important functions, and how do we achieve one?
Abstract: The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic $stat$ that is readily seen to be Mahonian. We give evidence showing that it is not equal to any previously published statistic. Nor does its joint distribution with the standard Eulerian statistics $des$ and $exc$ appear to coincide with any known Euler-Mahonian pair.
A general construction of Skandera yields an Eulerian partner $ska$ such that $(ska, stat)$ is equidistributed with $(des, maj)$. However $ska$ itself appears not to be a known Eulerian statistic.
Several ideas for further research on this topic are listed.