We study the distribution of the major index with sign on some parabolic
quotients of the symmetric group, extending and generalizing simultaneously
results Gessel-Simion and Adin-Gessel-Roichman, and on some special trees that
we call rakes. We further consider and compute the distribution of the
flag-major index on some parabolic quotients of wreath products and other
related groups. All these distributions turn out to have very simple
factorization formulas.Comment: 12 page