Postprint version. Published in Journal of Combinatorial Theory, Series A, Volume 53, Issue 1, January 1, 1990, pages 53-67.
The definitive version is available at https://doi.org/10.1016/0097-3165(90)90019-S.
Recent progress made by Desarmenien and Foata in the area of permutation statistics indirectly points out a certain gap in the theory of sequence enumeration. The remedy of the situation lies in the consideration of some colorful extensions of the Simon Newcomb problem.