Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.20615 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913629159292928 |
|---|---|
| author | Gregory, Adam Hamaker, Zachary Yu, Tianyi |
| author_facet | Gregory, Adam Hamaker, Zachary Yu, Tianyi |
| contents | Lam, Lee and Shimozono recently introduced backstable double Grothendieck polynomials to represent $K$-theory classes of the infinite flag variety. They used them to define double $β$-Stanley symmetric functions, which expand into double stable Grothendieck functions with polynomial coefficients called double $β$-Edelman--Greene coefficients. Anderson proved these coefficients are $β$-Graham positive. For vexillary permutations, this is equivalent to a statement for skew flagged double $β$-Grothendieck functions. Working in this setting, we give a tableau formula for vexillary double $β$-Edelman--Greene coefficients that is manifestly $β$-Graham positive. Our formula demonstrates a finer notion of positivity than was previously known. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tableau formula for vexillary double Edelman--Greene coefficients Gregory, Adam Hamaker, Zachary Yu, Tianyi Combinatorics Lam, Lee and Shimozono recently introduced backstable double Grothendieck polynomials to represent $K$-theory classes of the infinite flag variety. They used them to define double $β$-Stanley symmetric functions, which expand into double stable Grothendieck functions with polynomial coefficients called double $β$-Edelman--Greene coefficients. Anderson proved these coefficients are $β$-Graham positive. For vexillary permutations, this is equivalent to a statement for skew flagged double $β$-Grothendieck functions. Working in this setting, we give a tableau formula for vexillary double $β$-Edelman--Greene coefficients that is manifestly $β$-Graham positive. Our formula demonstrates a finer notion of positivity than was previously known. |
| title | Tableau formula for vexillary double Edelman--Greene coefficients |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.20615 |