Schubitopes were introduced by Monical, Tokcan and Yong as a specific family of generalized permutohedra. It was proven by Fink, Mészáros and St. Dizier that Schubitopes are the Newton polytopes of the dual characters of flagged Weyl modules. Important cases of Schubitopes include the Newton polytopes of Schubert polynomials and key polynomials. In this paper, we develop a combinatorial rule to generate the vertices of Schubitopes. As an application, we show that the vertices of the Newton polytope of a key polynomial can be generated by permutations in a lower interval in the Bruhat order, settling a conjecture of Monical, Tokcan and Yong.

Schubitopes是由Monical，Tokcan和Yong引入的，是一个特定的广义变位体家族。Fink，Mészáros和St. Dizier证明了Schubitopes是标记的Weyl模块的双重特征的牛顿多面体。Schubitopes的重要情况包括Schubert多项式的Newton多项式和关键多项式。在本文中，我们开发了一个组合规则来生成Schubitopes的顶点。作为一个应用程序，我们证明了关键多项式的牛顿多边形的顶点可以通过以Bruhat顺序在较低的间隔内排列而产生，从而解决了Monical，Tokcan和Yong的猜想。