Enumeration and width of lattice polytopes by their number of lattice points
ABSTRACT: We study the enumeration of d-dimensional lattice polytopes with n lattice points, for fixed d and n>d. - We prove that in each dimension d there is a constant w(d) such that: for each n>d there exist only finitely many d-dimensional lattice polytopes with n lattice points and lattic...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/11497 |
| Acceso en línea: | http://hdl.handle.net/10902/11497 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometría discreta Politopos reticulares Anchura reticular Puntos reticulares Finitud Discrete geometry Lattice polytopes Lattice width Lattice points Finiteness |
| Sumario: | ABSTRACT: We study the enumeration of d-dimensional lattice polytopes with n lattice points, for fixed d and n>d. - We prove that in each dimension d there is a constant w(d) such that: for each n>d there exist only finitely many d-dimensional lattice polytopes with n lattice points and lattice width strictly larger than w(d). We show that w(4)=2. - In dimension 3 we develop an algorithm that enumerates the (finite) list of 3-dimensional lattice polytopes with n lattice points and lattice width strictly larger than 1, from the (finite) list of those with n-1 lattice points. We include codes that implement the algorithm in MATLAB, with which we have computed the lists of the polytopes with up to 11 lattice points. |
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