A method is described by which the enumeration of permutations of 1, 2, ... n with a prescribed sequence A of rises and falls, or a prescribed sequence B of inversions of order, or with both A and B, is effected in terms of numbers derived from the representation theory of the symmetric group. A connexion with Schensted pairs of standard Young tableaux is also discussed. © 1976.
Foulkes, H. O. (1976). Enumeration of permutations with prescribed up-down and inversion sequences. Discrete Mathematics, 15(3), 235–252. https://doi.org/10.1016/0012-365X(76)90028-5