Cancellation-free formula for 1432-avoiding permutations

Construct a cancellation-free formula for the standard elementary monomial expansion of the Schubert polynomial $\mathfrak{S}_w$ for every 1432-avoiding permutation $w$, preferably using pipe dreams.

Background

The authors explain that Gao proved that 1432-avoidance is equivalent to all reduced pipe dreams for a permutation being related by simple ladder moves. Since the proof of the single-SEM characterization relies on such moves, they ask whether this structure can yield an explicit cancellation-free SEM expansion formula for the broader class of 1432-avoiding permutations.

References

Motivated by this fact, we ask the following questions:

\begin{enumerate} \item Can we find a cancellation-free formula for the SEM expansion of $\mathfrak{S}_w$ in the case where $w$ is $1432$-avoiding, perhaps in terms of pipe dreams?

— Single-SEM Schubert Polynomials  (2503.03903 - Woodruff, 5 Mar 2025) in Section 4, Further Directions