Triangulations

Structures for Algorithms and Applications
Softcover Nachdruck of the original 1. Auflage 2010
ISBN: 978-3-662-50241-9
Verlag: Springer

Buch, Englisch, Band 25, 535 Seiten, Paperback, Format (B × H): 193 mm x 260 mm, Gewicht: 1276 g

Reihe: Algorithms and Computation in Mathematics

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

De Loera, Jesus

Santos, Francisco

Rambau, Joerg

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

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.

Über Autor(innen)

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".