Upper bounds of Schubert polynomials

Let w be a permutation of {1, 2, …, n}, and let D(w) be the Rothe diagram of w. The Schubert polynomial Sw(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathfrak{S}_w}\left(x \right)$\end{document} can be realized as the dual character of the flagged Weyl module associated with D(w). This implies the following coefficient-wise inequality: Minw(x)≤Sw(x)≤Maxw(x),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{Mi}}{{\rm{n}}_w}\left(x \right) \le {\mathfrak{S}_w}\left(x \right) \le {\rm{Ma}}{{\rm{x}}_w}\left(x \right),$$\end{document}