The Graphical Major Index
  A generalization of the classical statistics ``maj'' and ``inv'' (the major index and number of inversions) on words is introduced, parameterized by arbitrary graphs on the underlying alphabet. The question of characterizing those graphs that lead to equi-distributed "inv" and "maj" is posed and answered. 
Dominique Foata (Univ. of Strasbourg) and Doron Zeilberger (Temple   University)