Tower tableaux and Schubert polynomials

TL;DR

This paper characterizes balanced labelings via a sliding algorithm on tower diagrams, leading to new descriptions of Schubert polynomials and Stanley symmetric functions.

Contribution

It introduces a novel characterization of balanced labelings using a generalized Rothification algorithm and applies it to describe key symmetric functions.

Findings

Balanced labelings characterized by sliding algorithm

Descriptions of Schubert polynomials derived

Descriptions of Stanley symmetric functions derived

Abstract

We prove that the well-known condition of being a balanced labeling can be characterized in terms of the sliding algorithm on tower diagrams. The characterization involves a generalization of authors' Rothification algorithm. Using the characterization, we obtain descriptions of Schubert polynomials and Stanley symmetric functions.