On Formulas and Some Combinatorial Properties of Schubert Polynomials  

作　　者：Zerui Zhang Yuqun Chen 

机构地区：[1]School of Mathematical Sciences, South China Normal University Guangzhou 510631, China

出　　处：《Algebra Colloquium》2017年第4期647-672,共26页代数集刊（英文版）

摘　　要：By applying a Grobner-Shirshov basis of the symmetric group Sn, we give two formulas for Schubert polynomials, either of which involves only nonnegative monomials. We also prove some combinatorial properties of Schubert polynomials. As applications, we give two algorithms to calculate the structure constants for Schubert polynomials, one of which depends on Monk＇s formula.By applying a Grobner-Shirshov basis of the symmetric group Sn, we give two formulas for Schubert polynomials, either of which involves only nonnegative monomials. We also prove some combinatorial properties of Schubert polynomials. As applications, we give two algorithms to calculate the structure constants for Schubert polynomials, one of which depends on Monk＇s formula.

关 键 词：divided difference Schubert polynomial Grobner-Shirshov basis 

分 类 号：O1[理学—数学]