Jesus De Loera: Triangulations | Buch

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Cover: 9783642129704 | Triangulations | Structures for Algorithms and Applications | Buch

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Sprache: Englisch

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Beschreibung

Triangulations appear everywhere, from volume computations and meshing
to algebra and topology. This book studies the subdivisions and
triangulations of polyhedral regions and point sets and presents the
first comprehensive treatment of the theory of secondary polytopes and
related topics.
A central theme of the book is the use of the rich structure of the
space of triangulations to solve computational problems (e.g., counting
the number of triangulations or finding optimal triangulations with
respect to various criteria), and to establish connections to
applications in algebra, computer science, combinatorics, and
optimization.
With many examples and exercises, and with nearly five hundred
illustrations, the book gently guides readers through the properties
of the spaces of triangulations of "structured" (e.g., cubes, cyclic
polytopes, lattice polytopes) and "pathological" (e.g., disconnected
spaces of triangulations) situations using only elementary principles.

Über den Autor

J.A. De Loera is a professor of mathematics at the University of California, Davis. His work approaches difficult computational problems in discrete mathematics and optimization using tools from algebra and convex geometry. His research has been recognized by an Alexander von Humboldt Fellowship and several national and international grants. He is an associate editor of the journal "Discrete Optimization". Jörg Rambau is the chair professor of Wirtschaftsmathematik (Business Mathematics) at the Universität of Bayreuth since 2004. Before that he was associate head of the optimization department at the Zuse Institute Berlin (ZIB). His research encompasses problems in applied optimization, algorithmic discrete mathematics and combinatorial geometry. He is the creator of the state of the art program for triangulation computations TOPCOM. He is associate editor of the "Jahresberichte der Deutschen Mathematiker-Vereinigung". Francisco Santos, a professor at the Universidad de Cantabria Spain, received the Young Researcher award from the Universidad Complutense de Madrid in 2003 and was an invited speaker in the Combinatorics Section of the International Congress of Mathematicians in 2006. He is well-known for his explicit constructions of polytopes with disconnected spaces of triangulations, some of which are featured in this book. He is an editor of Springer Verlag's journal "Discrete and Computational Geometry".

Zusammenfassung

First comprehensive treatment of the theory of regular triangulations, secondary polytopes and related topics appearing in book form

Discusses the geometric structure behind the algorithms and shows new emerging applications

Theory discusses high-dimensional situations, an area that is not always covered in computational geometry

Step-by-step introduction assuming very little background

Hundreds of illustrations, examples, and exercises

Includes supplementary material: [...]

Inhaltsverzeichnis

Triangulations in Mathematics.- Configurations, Triangulations, Subdivisions, and Flips.- Life in Two Dimensions.- A Tool Box.- Regular Triangulations and Secondary Polytopes.- Some Interesting Configurations.- Some Interesting Triangulations.- Algorithmic Issues.- Further Topics.

Details

Erscheinungsjahr:	2010
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	552
Reihe:	Algorithms and Computation in Mathematics
Inhalt:	xiii 535 S.
ISBN-13:	9783642129704
ISBN-10:	3642129706
Sprache:	Englisch
Herstellernummer:	12605583
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	De Loera, Jesus Santos, Francisco Rambau, Joerg
Auflage:	2010
Hersteller:	Springer Berlin Springer Berlin Heidelberg Algorithms and Computation in Mathematics
Maße:	266 x 198 x 34 mm
Von/Mit:	Jesus De Loera (u. a.)
Erscheinungsdatum:	06.09.2010
Gewicht:	1,495 kg

preigu-id: 101203434