Inverse Kazhdan-Lusztig polynomials of matroids under deletion
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911187952730112 |
|---|---|
| author | Braden, Tom Ferroni, Luis Matherne, Jacob P. Nepal, Nutan |
| author_facet | Braden, Tom Ferroni, Luis Matherne, Jacob P. Nepal, Nutan |
| contents | We provide a deletion formula for the inverse Kazhdan--Lusztig polynomial and the inverse $Z$-polynomial of a matroid. Our formulas provide analogues to the deletion formulas of Braden--Vysogorets for Kazhdan--Lusztig and $Z$-polynomials. We discuss several consequences, which include closed formulas and recursions for these invariants on uniform matroids, projective geometries, glued cycles, and arbitrary matroids of corank $2$. As a relevant application of our deletion formula, we show the existence of a matroid of rank $19$ which disproves a conjecture of Xie and Zhang concerning a real-rootedness property of inverse Kazhdan--Lusztig polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse Kazhdan-Lusztig polynomials of matroids under deletion Braden, Tom Ferroni, Luis Matherne, Jacob P. Nepal, Nutan Combinatorics We provide a deletion formula for the inverse Kazhdan--Lusztig polynomial and the inverse $Z$-polynomial of a matroid. Our formulas provide analogues to the deletion formulas of Braden--Vysogorets for Kazhdan--Lusztig and $Z$-polynomials. We discuss several consequences, which include closed formulas and recursions for these invariants on uniform matroids, projective geometries, glued cycles, and arbitrary matroids of corank $2$. As a relevant application of our deletion formula, we show the existence of a matroid of rank $19$ which disproves a conjecture of Xie and Zhang concerning a real-rootedness property of inverse Kazhdan--Lusztig polynomials. |
| title | Inverse Kazhdan-Lusztig polynomials of matroids under deletion |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.01086 |