Schubert多项式理论是代数组合领域的前沿研究方向，是运用组合工具研究Hilbert第15问题（Schubert计数演算之严格基础）的核心结构。Grothendieck多项式是Schubert多项式在代数K-理论中的推广。本项目拟通过进一步发展处理Schubert多项式的方法和技巧，研究该领域的一些公开问题并试图得到Schubert多项式和Grothendieck多项式新的性质。.本项目主要研究Schubert多项式和Grothendieck多项式的组合性质，具体研究内容包括：研究Schubert多项式的不同组合模型之间的联系；构建Grothendieck多项式的杨表模型；研究Grothendieck多项式的不同次数项的关系。

Schubert polynomial is a project in the intersection of algebraic combinatorics, and represent the frontier of algebraic combinatorics. Schubert polynomials are the key structures of Hilbert’s 15th problem (a rigorous foundation of Schubert’s Enumerative Calculus). Grothendieck polynomials are the generalization of Schubert polynomials in K-theory. This project intends to further develop the methods and techniques for dealing with Schubert polynomials, study some open problems in this field and try to obtain new properties of Schubert polynomials and Grothendieck polynomials. .In this project, we aim to study the combinatorial properties of Schubert polynomials and Grothendieck polynomials，mainly including: investigate the relation between different combinatorial models of Schubert polynomials; build a tableau model for Grothendieck polynomials; explore the relations between different terms of Grothendieck polynomials.