On Formulas and Some Combinatorial Properties of Schubert Polynomials

• 来源期刊: 代数集刊（英文版）
• 关键词: divided difference Schubert polynomial Gr(o)bner-Shirshov basis
• 年，卷（期）: 2017,（4）
• 页码范围: 647-672
• 页数: 26页
• 语种: 英文
• DOI: 10.1142/S1005386717000438

摘要

By applying a Gr(o)bner-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 calcnlate the structure constants for Schubert polynomials,one of which depends on Monk's formula.