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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.

Existence of Unimodular Triangulations-Positive Results

2021 Algebra, Abstract
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Release : 2021
Genre : Algebra, Abstract
Kind : eBook
Book Rating : 308/5 ( 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. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Positive Gaussian Kernels Also Have Gaussian Minimizers

2022-04-08 Mathematics
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Release : 2022-04-08
Genre : Mathematics
Kind : eBook
Book Rating : 433/5 ( reviews)

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Book Synopsis Positive Gaussian Kernels Also Have Gaussian Minimizers by : Franck Barthe

Download or read book Positive Gaussian Kernels Also Have Gaussian Minimizers written by Franck Barthe. This book was released on 2022-04-08. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Handbook of Discrete and Computational Geometry

2017-11-22 Computers
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Release : 2017-11-22
Genre : Computers
Kind : eBook
Book Rating : 421/5 ( reviews)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth. This book was released on 2017-11-22. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

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