Derivatives of padded Schubert polynomials through pipe dreams
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915448076894208 |
|---|---|
| author | Dennin, Hugh |
| author_facet | Dennin, Hugh |
| contents | In recent work, Hamaker, Pechenik, Speyer, and Weigandt showed that a certain differential operator $\nabla$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivatives of padded Schubert polynomials through pipe dreams Dennin, Hugh Combinatorics 05A19 (Primary) 05E05, 14N15 (Secondary) In recent work, Hamaker, Pechenik, Speyer, and Weigandt showed that a certain differential operator $\nabla$ 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. |
| title | Derivatives of padded Schubert polynomials through pipe dreams |
| topic | Combinatorics 05A19 (Primary) 05E05, 14N15 (Secondary) |
| url | https://arxiv.org/abs/2508.11879 |