Real-rootedness of the type A minuscule polynomials
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914859746066432 |
|---|---|
| author | Ding, Ming-Jian Zeng, Jiang |
| author_facet | Ding, Ming-Jian Zeng, Jiang |
| contents | We prove two recent conjectures of Bourn and Erickson (2023) regarding the real-rootedness of a certain family of polynomials $N_n(t)$ as well as the sum of their coefficients. These polynomials arise as the numerators of generating functions in the context of the discrete one-dimensional earth mover's distance (EMD) and have also connection to the Wiener index of minuscule lattices. We also prove that the coefficients of $N_n(x)$ are asymptotically normal, the coefficient matrix of $N_n(x)$ is totally positive and the polynomial sequence $N_n(x)$'s is $x$-log-concave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16782 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Real-rootedness of the type A minuscule polynomials Ding, Ming-Jian Zeng, Jiang Combinatorics 05A15, 05A10, 15B36, 62E20, 05A19 We prove two recent conjectures of Bourn and Erickson (2023) regarding the real-rootedness of a certain family of polynomials $N_n(t)$ as well as the sum of their coefficients. These polynomials arise as the numerators of generating functions in the context of the discrete one-dimensional earth mover's distance (EMD) and have also connection to the Wiener index of minuscule lattices. We also prove that the coefficients of $N_n(x)$ are asymptotically normal, the coefficient matrix of $N_n(x)$ is totally positive and the polynomial sequence $N_n(x)$'s is $x$-log-concave. |
| title | Real-rootedness of the type A minuscule polynomials |
| topic | Combinatorics 05A15, 05A10, 15B36, 62E20, 05A19 |
| url | https://arxiv.org/abs/2308.16782 |