A bijective proof of Kohnert's rule for Schubert polynomials
Combinatorics
2022-05-24 v2 Algebraic Geometry
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.
Cite
@article{arxiv.2003.01211,
title = {A bijective proof of Kohnert's rule for Schubert polynomials},
author = {Sami H. Assaf},
journal= {arXiv preprint arXiv:2003.01211},
year = {2022}
}
Comments
8 pages, 7 figures (examples added, minor corrections)