Characterization of two-term SEM expansions

Characterize the permutations $w\in S_n$ for which the SEM expansion of the Schubert polynomial $\mathfrak{S}_w$ has exactly two terms, preferably by a simple structural description.

Background

After asking for quantitative bounds on the number of terms in SEM expansions, the authors isolate the first nontrivial case as a separate question: identifying all permutations whose SEM expansion consists of exactly two terms. This seeks a pattern- or structural characterization analogous to the paper’s single-SEM theorem.