Large final polynomials from integer programming
We introduce a new method for finding a non-realizability certificate of a simplicial sphere S. It enables us to prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere by Zheng, a family of highly neighborly centrally symmetric spheres by Novik and Zheng, and several comb...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/362955 |
| Acceso en línea: | https://hdl.handle.net/2117/362955 https://dx.doi.org/10.1145/3511528.3511533 |
| Access Level: | acceso abierto |
| Palabra clave: | Integer programming Programació en nombres enters Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica |
| Sumario: | We introduce a new method for finding a non-realizability certificate of a simplicial sphere S. It enables us to prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere by Zheng, a family of highly neighborly centrally symmetric spheres by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos. The method, implemented in the polymake framework, uses integer programming to find a monomial combination of classical 3-term Plücker relations that must be positive in any realization of S; but since this combination should also vanish identically, the realization cannot exist. Previous approaches by Firsching, implemented using SCIP, and by Gouveia, Macchia and Wiebe, implemented using Singular and Macaulay2, are not able to process these examples. |
|---|