  Kohnert proposed the first monomial positive formula for Schubert polynomials
as the generating polynomial for certain unit cell diagrams obtained from the
Rothe diagram of a permutation. Billey, Jockusch and Stanley gave the first
proven formula for Schubert polynomials as the generating polynomial for
compatible sequences of reduced words of a permutation. In this paper, we give
an explicit bijection between these two models, thereby definitively proving
Kohnert's rule for Schubert polynomials.
