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September 24, 2025Open Access

Derivatives of padded Schubert polynomials through pipe dreams

Key Points

New proof shows that the dual differential operator positively expands padded Schubert polynomials.
This result is based on the combinatorial structure of pipe dreams, a critical aspect of the argument.
Prior findings by Gaetz and Tung on the positivity of action on Schubert polynomials are confirmed and extended here.
The work builds on previous studies while providing fresh insights into the interplay between combinatorics and symmetric functions.

Abstract

In recent work, Hamaker, Pechenik, Speyer, and Weigandt showed that a certain differential operator expands positively in the basis of Schubert polynomials. For π a dominant permutation, Gaetz and Tung showed an analogous positivity result holds for a dual differential operator Δ acting on π-padded Schubert polynomials. In this paper, we provide a new proof of the result of Gaetz and Tung using the combinatorics of pipe dreams.

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Cite This Study

Hugh Dennin (Sat,) studied this question.

synapsesocial.com/papers/68d6e1978b2b6861e4c4031d https://doi.org/https://doi.org/10.48550/arxiv.2508.11879

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