Schubert polynomials, 132-patterns, and Stanley's conjecture

TL;DR

This paper establishes a lower bound on the sum of coefficients of Schubert polynomials based on 132-pattern containment, motivated by Stanley's conjecture, linking pattern avoidance to polynomial coefficients.

Contribution

It provides a new lower bound for Schubert polynomial coefficients related to 132-patterns, advancing understanding of Stanley's conjecture.

Findings

Lower bound for Schubert polynomial coefficients established

Connection between 132-patterns and polynomial coefficient sums

Progress towards Stanley's conjecture in algebraic combinatorics

Abstract

Motivated by a recent conjecture of R. P. Stanley we offer a lower bound for the sum of the coefficients of a Schubert polynomial in terms of $132$-pattern containment.