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Triangulations

2010-08-16 Mathematics
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Release : 2010-08-16
Genre : Mathematics
Kind : eBook
Book Rating : 714/5 ( reviews)

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Book Synopsis Triangulations by : Jesus De Loera

Download or read book Triangulations written by Jesus De Loera. This book was released on 2010-08-16. Available in PDF, EPUB and Kindle. Book excerpt: Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.

Triangulations and Applications

2006-09-19 Mathematics
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Release : 2006-09-19
Genre : Mathematics
Kind : eBook
Book Rating : 618/5 ( reviews)

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Book Synopsis Triangulations and Applications by : Øyvind Hjelle

Download or read book Triangulations and Applications written by Øyvind Hjelle. This book was released on 2006-09-19. Available in PDF, EPUB and Kindle. Book excerpt: This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.

Triangulations of Oriented Matroids

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 693/5 ( reviews)

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Book Synopsis Triangulations of Oriented Matroids by : Francisco Santos

Download or read book Triangulations of Oriented Matroids written by Francisco Santos. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.

Triangulations and Simplicial Methods

2012-12-06 Business & Economics
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Release : 2012-12-06
Genre : Business & Economics
Kind : eBook
Book Rating : 750/5 ( reviews)

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Book Synopsis Triangulations and Simplicial Methods by : Chuangyin Dang

Download or read book Triangulations and Simplicial Methods written by Chuangyin Dang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations underlying them. This monograph describes some recent developments in triangulations and simplicial methods. It includes the D1-triangulation and its applications to simplicial methods. As a result, efficiency of simplicial methods has been improved significantly. Thus more effective simplicial methods have been developed.

Existence of Unimodular Triangulations–Positive Results

2021-07-21 Education
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Release : 2021-07-21
Genre : Education
Kind : eBook
Book Rating : 169/5 ( reviews)

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Book Synopsis Existence of Unimodular Triangulations–Positive Results by : Christian Haase

Download or read book Existence of Unimodular Triangulations–Positive Results written by Christian Haase. This book was released on 2021-07-21. Available in PDF, EPUB and Kindle. Book excerpt: Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.

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