@phdthesis{10902/11497,
year = {2017},
month = {6},
url = {http://hdl.handle.net/10902/11497},
abstract = {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.},
abstract = {RESUMEN: 
Estudiamos la enumeración de politopos reticulares d-dimensionales con n puntos reticulares, para d y n>d fijados. 

-	Demostramos que en cada dimensión d existe una constante w(d) tal que: para cada n>d existe sólo un número finito de politopos reticulares d-dimensionales con n puntos reticulares y anchura reticular estrictamente mayor que w(d). Se demuestra que w(4)=2.

-	En dimensión 3 elaboramos un algoritmo que calcula la lista (finita) de politopos reticulares 3-dimensionales con n puntos reticulares y de anchura reticular estrictamente mayor que 1, a partir de la lista (finita) de los que tienen n-1 puntos reticulares.
Se adjuntan códigos que implementan dicho algoritmo en MATLAB, y con los que se han calculado las listas de dichos politopos con hasta 11 puntos reticulares.},
organization = {This thesis has been developed under the following scholarships and project grants of the Spanish Ministry of Economics and Competitiveness: MTM2011-22792 and MTM2014-54207-P; BES-2012-058920; EEBB-I-2014-08588 and EEBB-I-2016-10623. I also need to thank The European Science Foundation within the ACAT Project, for partially funding my research visit in Berlin.},
title = {Enumeration and width of lattice polytopes by their number of lattice points},
author = {Blanco Gómez, Mónica},
}