  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.
