A generalized major index statistic on tableaux

Abstract: We extend the family of statistics maj_d, introduced for permutations by Kadell (1985), to standard Young tableaux. At one extreme, we have the traditional Major index statistic maj_1 for tableaux. At the other end, maj_n = inv, the inversion statistic introduced by Haglund and Stevens (2006). This is answers a question of Assaf (2008), who defined maj_2 and maj_3 for tableaux.