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On Formulas and Some Combinatorial Properties of Schubert Polynomials

2017/05/23 by Zerui Zhang, Yuqun Chen · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Basis (linear algebra) #Commutative Algebra and Its Applications #Constant (computer programming) #Schubert calculus #Schubert polynomial #Schubert variety #Structure constants #Symmetric group #math.RA #msc:05E05 #msc:05E15 #msc:14M15

paper · pdf · doi:10.1142/s1005386717000438

published in Algebra Colloquium 24(04), 647-672 (World Scientific) · 32 pages

arxiv created 2017/05/23 · openalex created_date 2017/06/05 · arxiv updated 2017/09/15 · openalex publication_date 2017/11/15 · openalex updated_date 2026/08/05

Abstract

By applying a Gröbner-Shirshov basis of the symmetric group S n , 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.

Citations