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PreprintarXiv licencearXiv

Lattice-free Schubitopes

  • Jinren Dou
  • Neil J. Y. Fan
  • Kunwen Liu
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Abstract

In this paper, we provide a simple criterion for the Schubitope 𝒮D associated to a diagram D to be lattice-free. We further show that 𝒮D 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 Sw(x) and the Grothendieck polynomial Gw(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.

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Cite

BibTeXRIS
BibTeX
@misc{dou2026latticefree,
  title = {{Lattice-free Schubitopes}},
  author = {Jinren Dou and Neil J. Y. Fan and Kunwen Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.10016},
  eprint = {2605.10016},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.10016},
}
RIS
TY  - UNPB
TI  - Lattice-free Schubitopes
AU  - Jinren Dou
AU  - Neil J. Y. Fan
AU  - Kunwen Liu
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2605.10016
UR  - https://arxiv.org/abs/2605.10016
AB  - In this paper, we provide a simple criterion for the Schubitope 𝒮_D associated to a diagram D to be lattice-free. We further show that 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 S_w(x) and the Grothendieck polynomial 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.
ER  -