A bijective proof of Kohnert's rule for Schubert polynomials
arXiv:2003.01211 · doi:10.5070/c62156877
Abstract
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.
8 pages, 7 figures (examples added, minor corrections)