Forest Polynomials and Pattern Avoidance
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917246978228224 |
|---|---|
| author | Guo, Annie Woodruff, Dora |
| author_facet | Guo, Annie Woodruff, Dora |
| contents | Forest polynomials, recently introduced by Nadeau and Tewari, can be thought of as a quasisymmetric analogue for Schubert polynomials. They have already been shown to exhibit interesting interactions with Schubert polynomials; for example, Schubert polynomials decompose positively into forest polynomials. We further describe this relationship by showing that a Schubert polynomial $\mathfrak{S}_w$ is a forest polynomial exactly when $w$ avoids a set of $6$ patterns. This result adds to the long list of properties of Schubert polynomials that are controlled by pattern avoidance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forest Polynomials and Pattern Avoidance Guo, Annie Woodruff, Dora Combinatorics Forest polynomials, recently introduced by Nadeau and Tewari, can be thought of as a quasisymmetric analogue for Schubert polynomials. They have already been shown to exhibit interesting interactions with Schubert polynomials; for example, Schubert polynomials decompose positively into forest polynomials. We further describe this relationship by showing that a Schubert polynomial $\mathfrak{S}_w$ is a forest polynomial exactly when $w$ avoids a set of $6$ patterns. This result adds to the long list of properties of Schubert polynomials that are controlled by pattern avoidance. |
| title | Forest Polynomials and Pattern Avoidance |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.04036 |