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Dissertations / Theses on the topic 'Lattice polytope'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Consult the top 31 dissertations / theses for your research on the topic 'Lattice polytope.'

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1

Hofmann, Jan [Verfasser]. "Three interesting lattice polytope problems / Jan Hofmann." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/1153008092/34.

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2

Borger, Christopher Verfasser], and Benjamin [Gutachter] [Nill. "Mixed lattice polytope theory with a view towards sparse polynomial systems / Christopher Borger ; Gutachter: Benjamin Nill." Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2020. http://d-nb.info/1220034908/34.

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3

Borger, Christopher [Verfasser], and Benjamin [Gutachter] Nill. "Mixed lattice polytope theory with a view towards sparse polynomial systems / Christopher Borger ; Gutachter: Benjamin Nill." Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2020. http://nbn-resolving.de/urn:nbn:de:gbv:ma9:1-1981185920-347964.

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4

Meyer, Marie. "Polytopes Associated to Graph Laplacians." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/54.

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Graphs provide interesting ways to generate families of lattice polytopes. In particular, one can use matrices encoding the information of a finite graph to define vertices of a polytope. This dissertation initiates the study of the Laplacian simplex, PG, obtained from a finite graph G by taking the convex hull of the columns of the Laplacian matrix for G. The Laplacian simplex is extended through the use of a parallel construction with a finite digraph D to obtain the Laplacian polytope, PD. Basic properties of both families of simplices, PG and PD, are established using techniques from Ehrha

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5

Webb, Kerri. "Counting Bases." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1120.

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A theorem of Edmonds characterizes when a pair of matroids has a common basis. Enumerating the common bases of a pair of matroid is a much harder problem, and includes the #P-complete problem of counting the number of perfect matchings in a bipartite graph. We focus on the problem of counting the common bases in pairs of regular matroids, and describe a class called <i>Pfaffian matroid pairs</i> for which this enumeration problem can be solved. We prove that when a pair of regular matroids is non-Pfaffian, there is a set of common bases which certifies this, and that the number of bases

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6

Gay, Joël. "Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS209/document.

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La combinatoire algébrique est le champ de recherche qui utilise des méthodes combinatoires et des algorithmes pour étudier les problèmes algébriques, et applique ensuite des outils algébriques à ces problèmes combinatoires. L’un des thèmes centraux de la combinatoire algébrique est l’étude des permutations car elles peuvent être interprétées de bien des manières (en tant que bijections, matrices de permutations, mais aussi mots sur des entiers, ordre totaux sur des entiers, sommets du permutaèdre…). Cette riche diversité de perspectives conduit alors aux généralisations suivantes du groupe sy

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7

Lundman, Anders. "Classifying Lattice Polytopes." Licentiate thesis, KTH, Matematik (Avd.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-134707.

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This thesis consists of two papers in toric geometry. In Paper A we provide a complete classification up to isomorphism of all smooth convex lattice 3- polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining four are obtained as inverse stellar subdivisions of such polytopes. We derive a classification, up to isomorphism, of all complete embeddings of smooth toric threefolds in PN where N ≤ 15. Again we have in total 103 such embeddings. Of these, 99 are projective bundles embedded

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8

Codenotti, Giulia [Verfasser]. "Covering properties of lattice polytopes / Giulia Codenotti." Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1205735569/34.

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9

Balletti, Gabriele. "Classifications and volume bounds of lattice polytopes." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-139823.

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In this licentiate thesis we study relations among invariants of lattice polytopes, with particular focus on bounds for the volume.In the first paper we give an upper bound on the volume vol(P^*) of a polytope P^* dual to a d-dimensional lattice polytope P with exactly one interiorlattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. In the second paper we classify the three-dimensional latti

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10

Akhtar, Mohammad Ehtisham. "Mutations of Laurent polynomials and lattice polytopes." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/28115.

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It has been conjectured that Fano manifolds correspond to certain Laurent polynomials under Mirror Symmetry. This correspondence predicts that the regularized quantum period of a Fano manifold coincides with the classical period of a Laurent polynomial mirror. This correspondence is not one-to-one, as many different Laurent polynomials can have the same classical period; it should become one-to-one after imposing the correct equivalence relation on Laurent polynomials. In this thesis we introduce what we believe to be the correct notion of equivalence: this is algebraic mutation of Laurent pol

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11

Paffenholz, Andreas. "Constructions for posets, lattices, and polytopes." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975678299.

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12

Moustrou, Philippe. "Geometric distance graphs, lattices and polytopes." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0802/document.

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Un graphe métrique G(X;D) est un graphe dont l’ensemble des sommets est l’ensemble X des points d’un espace métrique (X; d), et dont les arêtes relient les paires fx; yg de sommets telles que d(x; y) 2 D. Dans cette thèse, nous considérons deux problèmes qui peuvent être interprétés comme des problèmes de graphes métriques dans Rn. Premièrement, nous nous intéressons au célèbre problème d’empilements de sphères, relié au graphe métrique G(Rn; ]0; 2r[) pour un rayon de sphère r donné. Récemment, Venkatesh a amélioré d’un facteur log log n la meilleure borne inférieure connue pour un empilement

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13

Harrison, Anthony Westbrook. "Algorithms for Computing the Lattice Size." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1529781033957183.

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14

Kruse, Michael. "Lattice QCD Optimization and Polytopic Representations of Distributed Memory." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112198/document.

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La physique actuelle cherche, à côté des expériences, à vérifier et déduire les lois de la nature en simulant les modèles physiques sur d'énormes ordinateurs. Cette thèse explore comment accélérer ces simulations en améliorant les programmes qui les font tourner. L'application de référence est la chromodynamique quantique sur réseaux (LQCD pour "Lattice Quantum Chromodynamics"), une branche de la théorie quantique des champs, tournant sur le plus récent des supercalculateurs d'IBM, le Blue Gene/Q.Dans un premier temps, on améliore le code source de tmLQCD, un programme de LQCD, dont l'opératio

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15

Davis, Brian. "Lattice Simplices: Sufficiently Complicated." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/60.

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Simplices are the "simplest" examples of polytopes, and yet they exhibit much of the rich and subtle combinatorics and commutative algebra of their more general cousins. In this way they are sufficiently complicated --- insights gained from their study can inform broader research in Ehrhart theory and associated fields. In this dissertation we consider two previously unstudied properties of lattice simplices; one algebraic and one combinatorial. The first is the Poincar\'e series of the associated semigroup algebra, which is substantially more complicated than the Hilbert series of that same a

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16

Shipman, Barbara Anne. "Convex polytopes and duality in the geometry of the full Kostant-Toda lattice." Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187199.

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Our study describes the structure of the completely integrable system known as the full Kostant-Toda lattice in terms of the rich geometry of complex generalized flag manifolds and the information encoded in their momentum polytopes. The space in which the system evolves is a Poisson manifold which is essentially the dual of a Borel subalgebra of a Lie algebra, and the symplectic leaves are the coadjoint orbits. We extend the results of Ercolani, Flaschka, and Singer in (4) in which an embedding of an isospectral submanifold of the phase space into the flag manifold is used to study the geomet

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17

Brinkmann, Philip [Verfasser]. "f-Vector Spaces of Polytopes, Spheres, and Eulerian Lattices / Philip Brinkmann." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1118526864/34.

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18

Alajmi, Abdulrahman N. "On The Lattice Size With Respect To The Standard Simplex in 3D." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1598893373379275.

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19

Kohl, Florian [Verfasser]. "Lattice Polytopes - Applications and Properties : Ehrhart Theory, Graph Colorings, and Level Algebras / Florian Kohl." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/1176639625/34.

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20

Schaller, Karin [Verfasser], and Victor V. [Akademischer Betreuer] Batyrev. "Stringy Invariants of Algebraic Varieties and Lattice Polytopes / Karin Schaller ; Betreuer: Victor V. Batyrev." Tübingen : Universitätsbibliothek Tübingen, 2019. http://d-nb.info/1181784190/34.

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21

Dadush, Daniel Nicolas. "Integer programming, lattice algorithms, and deterministic volume estimation." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44807.

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The main subject of this thesis is the development of new geometric tools and techniques for solving classic problems within the geometry of numbers and convex geometry. At a high level, the problems considered in this thesis concern the varied interplay between the continuous and the discrete, an important theme within computer science and operations research. The first subject we consider is the study of cutting planes for non-linear integer programs. Cutting planes have been implemented to great effect for linear integer programs, and so understanding their properties in more general settin

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22

Henze, Matthias [Verfasser], and Martin [Akademischer Betreuer] Henk. "Lattice point inequalities and face numbers of polytopes in view of central symmetry / Matthias Henze. Betreuer: Martin Henk." Magdeburg : Universitätsbibliothek, 2012. http://d-nb.info/105322771X/34.

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23

Le, Tran Bach. "On k-normality and regularity of normal projective toric varieties." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31531.

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We study the relationship between geometric properties of toric varieties and combinatorial properties of the corresponding lattice polytopes. In particular, we give a bound for a very ample lattice polytope to be k-normal. Equivalently, we give a new combinatorial bound for the Castelnuovo-Mumford regularity of normal projective toric varieties. We also give a new combinatorial proof for a special case of Reider's Theorem for smooth toric surfaces.

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24

Bureaux, Julien. "Méthodes probabilistes pour l'étude asymptotique des partitions entières et de la géométrie convexe discrète." Thesis, Paris 10, 2015. http://www.theses.fr/2015PA100160/document.

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Cette thèse se compose de plusieurs travaux portant sur l'énumération et le comportement asymptotique de structures combinatoires apparentées aux partitions d'entiers. Un premier travail s'intéresse aux partitions d'entiers bipartites, qui constituent une généralisation bidimensionnelle des partitions d'entiers. Des équivalents du nombre de partitions sont obtenus dans le régime critique où l'un des entiers est de l'ordre du carré de l'autre entier et au delà de ce régime critique. Ceci complète les résultats établis dans les années cinquante par Auluck, Nanda et Wright. Le deuxième travail tr

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25

v, Thaden Michael. "Unimodular Covers and Triangulations of Lattice Polytopes." Doctoral thesis, 2008. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2008061610.

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Diese Arbeit befasst sich mit der unimodularen Überdeckung und Triangulierung von Gitterpolytopen. Zentral ist in diesem Zusammenhang die Angabe einer möglichst guten oberen Schranke c0, so dass die Vielfachen cP eines Polytopes P für alle c>c0 eine unimodulare Überdeckung besitzen. Bruns und Gubeladze haben erstmals die Existenz einer solchen Schranke nachgewiesen und konnten sogar explizit eine solche in Abhängigkeit von der Dimension des Polytopes angeben. Allerdings war diese Schranke super-exponentiell. In dieser Arbeit wird nun u.a. eine polynomielle obere Schranke hergeleitet.

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26

Kölbl, Max. "Algebraic Properties of Lattice Polytopes Coming From Graphs." 2021. https://ul.qucosa.de/id/qucosa%3A73880.

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Die Arbeit besteht hauptsächlich aus zwei Teilen: einer Zusammenfassung kombinatorischer und algebraisch-geometrischer Themen (Gitterpolytope, torische (Gorenstein-)Varietäten, und Matroide), und einem Ergebnisteil. Letzerer besteht aus zwei Teilen. Im ersten Teil wird eine konstruktive Klassifikation von Multigraphen, deren graphisches Matroid ein Basispolytop erzeugt, das die Gorenstein-Eigenschaft erfüllt, erarbeitet. Im zweiten Teil wird ein Satz rekursiver Formeln, die die Ehrhartpolynome von symmetrischen Kantenpolytopen, die aus vollständig-biparten Graphen hervorgehen, zueinander in Be

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27

Thaden, Michael von [Verfasser]. "Unimodular covers and triangulations of lattice polytopes / vorgelegt von Michael v. Thaden." 2008. http://d-nb.info/989236234/34.

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28

Paffenholz, Andreas [Verfasser]. "Constructions for posets, lattices, and polytopes / vorgelegt von Andreas Paffenholz." 2005. http://d-nb.info/975678299/34.

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29

Haase, Christian [Verfasser]. "Lattice polytopes and triangulations : with applications to toric geometry / vorgelegt von Christian Alexander Haase." 2000. http://d-nb.info/959572430/34.

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30

Hong, Ngoc Binh. "Randomized integer convex hull." Doctoral thesis, 2021. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202102124020.

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The thesis deals with stochastic and algebraic aspects of the integer convex hull. In the first part, the intrinsic volumes of the randomized integer convex hull are investigated. In particular, we obtained an exact asymptotic order of the expected intrinsic volumes difference in a smooth convex body and a tight inequality for the expected mean width difference. In the algebraic part, an exact formula for the Bhattacharya function of complete primary monomial ideas in two variables is given. As a consequence, we derive an effective characterization for complete monomial ideals in two variables

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31

Wagner, Jan-Martin [Verfasser]. "Structure and lattice dynamics of GaN and AlN: ab-initio investigations of strained polytypes and superlattices / von Jan-Martin Wagner." 2008. http://d-nb.info/987743937/34.

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