Tower Diagrams and Pieri's Rule

2018/07/10 by Olcay Coşkun, Coşkun, Olcay, Müge Taşkın +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1807.03764

openalex publication_date 2018/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce an algorithm to describe Pieri's Rule for multiplication of Schubert polynomials. The algorithm uses tower diagrams introduced by the authors and another new algorithm that describes Monk's Rule. Our result is different from the well-known descriptions (and proofs) of the rule by Bergeron-Billey and Kogan-Kumar and uses Sottile's version of Pieri's Rule.

Related

• Tower tableaux and Schubert polynomials
• Growth Diagrams for the Schubert Multiplication
• Pieri rules for the K-theory of cominuscule Grassmannians
• Pieri and Murnaghan--Nakayama type Rules for Chern classes of Schubert Cells
• RC-graphs and a generalized Littlewood-Richardson rule