Tower Diagrams and Pieri's Rule

TL;DR

This paper presents a new algorithm using tower diagrams to describe Pieri's Rule for Schubert polynomial multiplication, offering an alternative to existing methods and incorporating Sottile's version.

Contribution

It introduces a novel algorithm based on tower diagrams for Pieri's Rule, differing from prior descriptions and proofs by Bergeron-Billey and Kogan-Kumar.

Findings

Developed a new tower diagram-based algorithm for Pieri's Rule

Provided an alternative proof approach using Sottile's version

Enhanced understanding of Schubert polynomial multiplication

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.