Schubert Products for Permutations with Separated Descents

We say that two permutations $\pi$ and $\rho$ have separated descents at position $k$ if has no before after $k$. give a counting formula, in terms of reduced word tableaux, for computing the structure constants products Schubert polynomials indexed by with descents, recognize these are certain Edelman-Greene coefficients. Our approach uses generalizations Sch\"utzenberger's jeu de taquin algorithm correspondence via bumpless pipe dreams.