Single SEM Schubert Polynomials

Abstract

We prove a pattern-avoidance characterization of $w \in S_n$ such that the Schubert polynomial $\mathfrak{S}_w$ is a standard elementary monomial. This characterization tells us which quantum Schubert polynomials admit the simplest explicit formulas. We solve a similar pattern-avoidance problem for complete homogeneous monomials.