Global ETD Search

1	Parallel Algorithms for Rational Cones and Affine Monoids / Parallele Algorithmen für rationale Kegel und affine Monoide Söger, Christof 22 April 2014 (has links) This thesis presents parallel algorithms for rational cones and affine monoids which pursue two main computational goals: finding the Hilbert basis, a minimal generating system of the monoid of lattice points of a cone; and counting elements degree-wise in a generating function, the Hilbert series. affine monoid rational cone normalization convex geometry Hilbert basis Hilbert series ddc:510
2	HILBERT BASES, DESCENT STATISTICS, AND COMBINATORIAL SEMIGROUP ALGEBRAS Olsen, McCabe J. 01 January 2018 (has links) The broad topic of this dissertation is the study of algebraic structure arising from polyhedral geometric objects. There are three distinct topics covered over three main chapters. However, each of these topics are further linked by a connection to the Eulerian polynomials. Chapter 2 studies Euler-Mahonian identities arising from both the symmetric group and generalized permutation groups. Specifically, we study the algebraic structure of unit cube semigroup algebra using Gröbner basis methods to acquire these identities. Moreover, this serves as a bridge between previous methods involving polyhedral geometry and triangulations with descent bases methods arising in representation theory. In Chapter 3, the aim is to characterize Hilbert basis elements of certain 𝒔-lecture hall cones. In particular, the main focus is the classification of the Hilbert bases for the 1 mod 𝑘 cones and the 𝓁-sequence cones, both of which generalize a previous known result. Additionally, there is much broader characterization of Hilbert bases in dimension ≤ 4 for 𝒖-generated Gorenstein lecture hall cones. Finally, Chapter 4 focuses on certain algebraic and geometric properties of 𝒔-lecture hall polytopes. This consists of partial classification results for the Gorenstein property, the integer-decomposition property, and the existence of regular, unimodular triangulations. Ehrhart theory lecture hall partitions descent statistics major index statistics Gröebner basis Hilbert basis Discrete Mathematics and Combinatorics
3	Pologrupy mřížových bodů / Semigroups of lattice points Scholle, Marek January 2012 (has links) The thesis deals with subsemigroups of (Nm 0 , +), a special discussion is later devoted to the cases m = 1, m = 2 and m = 3. We prove that a subsemigroup of Nm 0 is finitely generated if and only if its generated cone is finitely generated (equivalently polyhedral) and we describe basic topological properties of such cones. We give a few examples illustrating that conditions sufficient for finite generation in N2 0 can not be easily trans- ferred to higher dimensions. We define the Hilbert basis and the related notion of Carathéodory's rank. Besides their basic properties we prove that Carathédory's rank of a subsemigroup of Nm 0 , m = 1, 2, 3, is less than or equal to m. A particular attention is devoted to the subsemigroups containing non-trivial subsemigroups of "subtractive" elements.
4	Affine Monoids, Hilbert Bases and Hilbert Functions Koch, Robert 11 July 2003 (has links) The aim of this thesis is to introduce the reader to the theory of affine monoids and, thereby, to present some results. We therefore start with some auxiliary sections, containing general introductions to convex geometry, affine monoids and their algebras, Hilbert functions and Hilbert series. One central part of the thesis then is the description of an algorithm for computing the integral closure of an affine monoid. The algorithm has been implemented, in the computer program `normaliz´; it outputs the Hilbert basis and the Hilbert function of the integral closure (if the monoid is positive). Possible applications include: finding the lattice points in a lattice polytope, computing the integral closure of a monomial ideal and solving Diophantine systems of linear inequalities. The other main part takes up the notion of multigraded Hilbert function: we investigate the effect of the growth of the Hilbert function along arithmetic progressions (within the grading set) on global growth. This study is motivated by the case of a finitely generated module over a homogeneous ring: there, the Hilbert function grows with a degree which is well determined by the degree of the Hilbert polynomial (and the Krull dimension). affine monoid integral closure normalization Hilbert basis Hilbert function affine monoid algebra semigroup ring 13B22 13D40 13P99 20M25 52B20 27 - Mathematik ddc:510
5	Bases de Hilbert / Hilbert Basis Hashimoto, Marcelo 28 February 2007 (has links) Muitas relações min-max em otimização combinatória podem ser demonstradas através de total dual integralidade de sistemas lineares. O conceito algébrico de bases de Hilbert foi originalmente introduzido com o objetivo de melhor compreender a estrutura geral dos sistemas totalmente dual integrais. Resultados apresentados posteriormente mostraram que bases de Hilbert também são relevantes para a otimização combinatória em geral e para a caracterização de certas classes de objetos discretos. Entre tais resultados, foram provadas, a partir dessas bases, versões do teorema de Carathéodory para programação inteira. Nesta dissertação, estudamos aspectos estruturais e computacionais de bases de Hilbert e relações destas com programação inteira e otimização combinatória. Em particular, consideramos versões inteiras do teorema de Carathéodory e conjecturas relacionadas. / There are several min-max relations in combinatorial optimization that can be proved through total dual integrality of linear systems. The algebraic concept of Hilbert basis was originally introduced with the objective of better understanding the general structure of totally dual integral systems. Some results that were proved later have shown that Hilbert basis are also relevant to combinatorial optimization in a general manner and to characterize certain classes of discrete objects. Among such results, there are versions of Carathéodory\'s theorem for integer programming that were proved through those basis. In this dissertation, we study structural and computational aspects of Hilbert basis and their relations to integer programming and combinatorial optimization. In particular, we consider integer versions of Carathéodory\'s theorem and related conjectures. bases de Hilbert Carathéodory's theorem Carathéodory\'s theorem combinatorial optimization combinatorial optimization duality theorem duality theorem Hilbert basis Hilbert basis integer programming integer programming linear programming linear programming min-max relations min-max relations otimização combinatória programação inteira programação linear relações min-max teorema da dualidade teorema de Carathéodory total dual integralidade total dual integrality total dual integrality
6	Bases de Hilbert / Hilbert Basis Marcelo Hashimoto 28 February 2007 (has links) Muitas relações min-max em otimização combinatória podem ser demonstradas através de total dual integralidade de sistemas lineares. O conceito algébrico de bases de Hilbert foi originalmente introduzido com o objetivo de melhor compreender a estrutura geral dos sistemas totalmente dual integrais. Resultados apresentados posteriormente mostraram que bases de Hilbert também são relevantes para a otimização combinatória em geral e para a caracterização de certas classes de objetos discretos. Entre tais resultados, foram provadas, a partir dessas bases, versões do teorema de Carathéodory para programação inteira. Nesta dissertação, estudamos aspectos estruturais e computacionais de bases de Hilbert e relações destas com programação inteira e otimização combinatória. Em particular, consideramos versões inteiras do teorema de Carathéodory e conjecturas relacionadas. / There are several min-max relations in combinatorial optimization that can be proved through total dual integrality of linear systems. The algebraic concept of Hilbert basis was originally introduced with the objective of better understanding the general structure of totally dual integral systems. Some results that were proved later have shown that Hilbert basis are also relevant to combinatorial optimization in a general manner and to characterize certain classes of discrete objects. Among such results, there are versions of Carathéodory\'s theorem for integer programming that were proved through those basis. In this dissertation, we study structural and computational aspects of Hilbert basis and their relations to integer programming and combinatorial optimization. In particular, we consider integer versions of Carathéodory\'s theorem and related conjectures. bases de Hilbert otimização combinatória programação inteira programação linear relações min-max teorema da dualidade teorema de Carathéodory total dual integralidade Carathéodory's theorem combinatorial optimization duality theorem Hilbert basis integer programming linear programming min-max relations total dual integrality

1

Page generated in 0.0569 seconds