An Interesting New Mahonian Permutation Statistic

Mark C. Wilson
2010 Electronic Journal of Combinatorics  
The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic DIS 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 eul such that (eul, DIS) is equidistributed with (des, MAJ). However
more » ... eul itself appears not to be a known Eulerian statistic. Several ideas for further research on this topic are listed.
doi:10.37236/419 fatcat:c6pm435funfotopfoflv5eiy3i