Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.10016 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909031099006976 |
|---|---|
| author | Dou, Jinren Fan, Neil J. Y. Liu, Kunwen |
| author_facet | Dou, Jinren Fan, Neil J. Y. Liu, Kunwen |
| contents | In this paper, we provide a simple criterion for the Schubitope $\mathcal{S}_{D}$ associated to a diagram $D$ to be lattice-free. We further show that $\mathcal{S}_{D}$ is lattice-free if and only if its Ehrhart polynomial is equal to the product of Ehrhart polynomials of the Schubert matroid polytopes corresponding to each column of $D$. As applications, we obtain that the Newton polytopes of the Schubert polynomial $\mathfrak{S}_w(x)$ and the Grothendieck polynomial $\mathfrak{G}_w(x)$ are lattice-free if and only if $w$ avoids the patterns 1423, 1432, 13254, and confirm several conjectures by Mészáros, Setiabrata, and St.Dizier on the support of Grothendieck polynomials for this class of permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lattice-free Schubitopes Dou, Jinren Fan, Neil J. Y. Liu, Kunwen Combinatorics In this paper, we provide a simple criterion for the Schubitope $\mathcal{S}_{D}$ associated to a diagram $D$ to be lattice-free. We further show that $\mathcal{S}_{D}$ is lattice-free if and only if its Ehrhart polynomial is equal to the product of Ehrhart polynomials of the Schubert matroid polytopes corresponding to each column of $D$. As applications, we obtain that the Newton polytopes of the Schubert polynomial $\mathfrak{S}_w(x)$ and the Grothendieck polynomial $\mathfrak{G}_w(x)$ are lattice-free if and only if $w$ avoids the patterns 1423, 1432, 13254, and confirm several conjectures by Mészáros, Setiabrata, and St.Dizier on the support of Grothendieck polynomials for this class of permutations. |
| title | Lattice-free Schubitopes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.10016 |