PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
September 24, 20250 citationsOpen Access

Derivatives of padded Schubert polynomials through pipe dreams

View Full Paper
HDHugh Dennin

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.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Hugh Dennin (2025) studied this question.

synapsesocial.com/papers/68d6e1978b2b6861e4c4031dhttps://doi.org/10.48550/arxiv.2508.11879
Ask AI
Helpful
Bookmark
Share
View Full Paper