Resumen
Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope is reflexive. While these properties are of independent interest, the confluence of these properties is a source of active investigation due to conjectures regarding the unimodality of the h∗-polynomial. In this paper, we consider the Newton polytopes arising from two families of polynomials in algebraic combinatorics: Schur polynomials and inflated symmetric Grothendieck polynomi-als. In both cases, we prove that these polytopes have the integer decomposition property by using the fact that both families of polynomials have saturated Newton polytope. Furthermore, in both cases, we provide a complete characterization of when these polytopes are reflexive. We conclude with some explicit formulas and unimodality implications of the h∗-vector in the case of Schur polynomials.
| Idioma original | English |
|---|---|
| Número de artículo | P2.45 |
| Publicación | Electronic Journal of Combinatorics |
| Volumen | 28 |
| N.º | 2 |
| DOI | |
| Estado | Published - 2021 |
Nota bibliográfica
Publisher Copyright:© The authors.
Financiación
This work was completed in part at the 2019 Graduate Research Workshop in Combinatorics, which was supported in part by NSF grant #1923238, NSA grant #H98230-18-1-0017, a generous award from the Combinatorics Foundation, and Simons Foundation Collaboration Grants #426971 (to M. Ferrara) and #315347 (to J. Martin). Partially supported by University of Kansas General Research Fund. Partially supported by AMS-Simons Travel Grant. Partially supported by Simons Collaboration Grant. The authors would like to thank Federico Castillo and Semin Yoo for helpful discussions and contributions to the early stages of the project. We would also like to thank Michel Marcus and Avery St. Dizier for helpful comments on a previous version of the paper. This work was completed in part at the 2019 Graduate Research Workshop in Combinatorics, which was supported in part by NSF grant #1923238, NSA grant #H98230-18-1-0017, a generous award from the Combinatorics Foundation, and Simons Foundation Collaboration Grants #426971 (to M. Ferrara) and #315347 (to J. Martin). \u2217Partially supported by University of Kansas General Research Fund. \u2020Partially supported by AMS-Simons Travel Grant. \u2021Partially supported by Simons Collaboration Grant.
| Financiadores | Número del financiador |
|---|---|
| Combinatorics Foundation | |
| AMS-Simons | |
| University of Kansas and University of Kansas Cancer Center | |
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | 1923238 |
| National Security Agency | 98230-18-1-0017 |
| Simons Foundation | 426971, 315347 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics