Postprint version. Published in Journal of Combinatorial Theory, Series A, Volume 31, January 1, 1981, pages 175-183.
Copyright © 1981 Elsevier.
The r-major index is a new permutation statistic that is suggested by the work of Carlitz and Gausner on Foulkes' skew hook rule for computing the r-Eulerian numbers. The new statistic (1) generalizes both the major index and the inversion number of a permutation and (2) leads to a q-analog of the r-Eulerian numbers.